Cálculo Exemplos

$\sum_{j = 1}^{4} - \frac{2}{2 j + 3}$

Etapa 1

Expanda a série para cada valor de $j$ .

$- \frac{2}{2 \cdot 1 + 3} - \frac{2}{2 \cdot 2 + 3} - \frac{2}{2 \cdot 3 + 3} - \frac{2}{2 \cdot 4 + 3}$

Etapa 2

Simplifique.

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Etapa 2.1

Encontre o denominador comum.

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Etapa 2.1.1

Multiplique $\frac{2}{2 \cdot 1 + 3}$ por $\frac{\frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 \cdot 1 + 3}}{\frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 \cdot 1 + 3}}$ .

$- (\frac{2}{2 \cdot 1 + 3} \cdot \frac{\frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 \cdot 1 + 3}}{\frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 \cdot 1 + 3}}) - \frac{2}{2 \cdot 2 + 3} - \frac{2}{2 \cdot 3 + 3} - \frac{2}{2 \cdot 4 + 3}$

Etapa 2.1.2

$- \frac{2 \frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 + 3}}{(2 + 3) \frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 + 3}} - \frac{2}{2 \cdot 2 + 3} - \frac{2}{2 \cdot 3 + 3} - \frac{2}{2 \cdot 4 + 3}$

Etapa 2.1.3

Multiplique $\frac{2}{2 \cdot 2 + 3}$ por $\frac{(2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{(2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}$ .

$- \frac{2 \frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 + 3}}{(2 + 3) \frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 + 3}} - (\frac{2}{2 \cdot 2 + 3} \cdot \frac{(2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{(2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}) - \frac{2}{2 \cdot 3 + 3} - \frac{2}{2 \cdot 4 + 3}$

Etapa 2.1.4

Multiplique $\frac{2}{2 \cdot 2 + 3}$ por $\frac{(2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{(2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}$ .

Etapa 2.1.5

Multiplique $\frac{2}{2 \cdot 3 + 3}$ por $\frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3)}{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3)}$ .

$- \frac{2 \frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 + 3}}{(2 + 3) \frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 + 3}} - \frac{2 ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3))}{(2 \cdot 2 + 3) ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3))} - (\frac{2}{2 \cdot 3 + 3} \cdot \frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3)}{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3)}) - \frac{2}{2 \cdot 4 + 3}$

Etapa 2.1.6

Multiplique $\frac{2}{2 \cdot 3 + 3}$ por $\frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3)}{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3)}$ .

$- \frac{2 \frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 + 3}}{(2 + 3) \frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 + 3}} - \frac{2 ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3))}{(2 \cdot 2 + 3) ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3))} - \frac{2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3))}{(2 \cdot 3 + 3) ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3))} - \frac{2}{2 \cdot 4 + 3}$

Etapa 2.1.7

Multiplique $\frac{2}{2 \cdot 4 + 3}$ por $\frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3)}{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3)}$ .

$- \frac{2 \frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 + 3}}{(2 + 3) \frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 + 3}} - \frac{2 ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3))}{(2 \cdot 2 + 3) ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3))} - \frac{2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3))}{(2 \cdot 3 + 3) ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3))} - (\frac{2}{2 \cdot 4 + 3} \cdot \frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3)}{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3)})$

Etapa 2.1.8

Multiplique $\frac{2}{2 \cdot 4 + 3}$ por $\frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3)}{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3)}$ .

$- \frac{2 \frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 + 3}}{(2 + 3) \frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 + 3}} - \frac{2 ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3))}{(2 \cdot 2 + 3) ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3))} - \frac{2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3))}{(2 \cdot 3 + 3) ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3))} - \frac{2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 \cdot 4 + 3) ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}$

Etapa 2.1.9

Reordene os fatores de $(2 + 3) \frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 + 3}$ .

$- \frac{2 \frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 + 3}}{\frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 + 3} (2 + 3)} - \frac{2 ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3))}{(2 \cdot 2 + 3) ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3))} - \frac{2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3))}{(2 \cdot 3 + 3) ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3))} - \frac{2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 \cdot 4 + 3) ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}$

Etapa 2.1.10

Multiplique $2$ por $2$ .

$- \frac{2 \frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 + 3}}{\frac{(2 + 3) (4 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 + 3} (2 + 3)} - \frac{2 ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3))}{(2 \cdot 2 + 3) ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3))} - \frac{2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3))}{(2 \cdot 3 + 3) ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3))} - \frac{2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 \cdot 4 + 3) ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}$

Etapa 2.1.11

Multiplique $2$ por $3$ .

$- \frac{2 \frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 + 3}}{\frac{(2 + 3) (4 + 3) (6 + 3) (2 \cdot 4 + 3)}{2 + 3} (2 + 3)} - \frac{2 ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3))}{(2 \cdot 2 + 3) ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3))} - \frac{2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3))}{(2 \cdot 3 + 3) ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3))} - \frac{2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 \cdot 4 + 3) ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}$

Etapa 2.1.12

Multiplique $2$ por $4$ .

$- \frac{2 \frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 + 3}}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} - \frac{2 ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3))}{(2 \cdot 2 + 3) ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3))} - \frac{2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3))}{(2 \cdot 3 + 3) ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3))} - \frac{2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 \cdot 4 + 3) ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}$

Etapa 2.1.13

Reordene os fatores de $(2 \cdot 2 + 3) ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3))$ .

$- \frac{2 \frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 + 3}}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} - \frac{2 ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3))}{(2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3) (2 + 3)} - \frac{2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3))}{(2 \cdot 3 + 3) ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3))} - \frac{2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 \cdot 4 + 3) ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}$

Etapa 2.1.14

Multiplique $2$ por $2$ .

$- \frac{2 \frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 + 3}}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} - \frac{2 ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3))}{(4 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3) (2 + 3)} - \frac{2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3))}{(2 \cdot 3 + 3) ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3))} - \frac{2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 \cdot 4 + 3) ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}$

Etapa 2.1.15

Multiplique $2$ por $3$ .

$- \frac{2 \frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 + 3}}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} - \frac{2 ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3))}{(4 + 3) (6 + 3) (2 \cdot 4 + 3) (2 + 3)} - \frac{2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3))}{(2 \cdot 3 + 3) ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3))} - \frac{2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 \cdot 4 + 3) ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}$

Etapa 2.1.16

Multiplique $2$ por $4$ .

$- \frac{2 \frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 + 3}}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} - \frac{2 ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3))}{(4 + 3) (6 + 3) (8 + 3) (2 + 3)} - \frac{2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3))}{(2 \cdot 3 + 3) ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3))} - \frac{2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 \cdot 4 + 3) ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}$

Etapa 2.1.17

Reordene os fatores de $(2 \cdot 3 + 3) ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3))$ .

$- \frac{2 \frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 + 3}}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} - \frac{2 ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3))}{(4 + 3) (6 + 3) (8 + 3) (2 + 3)} - \frac{2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3))}{(2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3) (2 + 3)} - \frac{2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 \cdot 4 + 3) ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}$

Etapa 2.1.18

Multiplique $2$ por $2$ .

$- \frac{2 \frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 + 3}}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} - \frac{2 ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3))}{(4 + 3) (6 + 3) (8 + 3) (2 + 3)} - \frac{2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3))}{(4 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3) (2 + 3)} - \frac{2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 \cdot 4 + 3) ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}$

Etapa 2.1.19

Multiplique $2$ por $3$ .

$- \frac{2 \frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 + 3}}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} - \frac{2 ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3))}{(4 + 3) (6 + 3) (8 + 3) (2 + 3)} - \frac{2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3))}{(4 + 3) (6 + 3) (2 \cdot 4 + 3) (2 + 3)} - \frac{2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 \cdot 4 + 3) ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}$

Etapa 2.1.20

Multiplique $2$ por $4$ .

$- \frac{2 \frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 + 3}}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} - \frac{2 ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3))}{(4 + 3) (6 + 3) (8 + 3) (2 + 3)} - \frac{2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3))}{(4 + 3) (6 + 3) (8 + 3) (2 + 3)} - \frac{2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 \cdot 4 + 3) ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}$

Etapa 2.1.21

Reordene os fatores de $(2 \cdot 4 + 3) ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))$ .

$- \frac{2 \frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 + 3}}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} - \frac{2 ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3))}{(4 + 3) (6 + 3) (8 + 3) (2 + 3)} - \frac{2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3))}{(4 + 3) (6 + 3) (8 + 3) (2 + 3)} - \frac{2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3) (2 + 3)}$

Etapa 2.1.22

Multiplique $2$ por $2$ .

$- \frac{2 \frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 + 3}}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} - \frac{2 ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3))}{(4 + 3) (6 + 3) (8 + 3) (2 + 3)} - \frac{2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3))}{(4 + 3) (6 + 3) (8 + 3) (2 + 3)} - \frac{2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(4 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3) (2 + 3)}$

Etapa 2.1.23

Multiplique $2$ por $3$ .

$- \frac{2 \frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 + 3}}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} - \frac{2 ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3))}{(4 + 3) (6 + 3) (8 + 3) (2 + 3)} - \frac{2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3))}{(4 + 3) (6 + 3) (8 + 3) (2 + 3)} - \frac{2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(4 + 3) (6 + 3) (2 \cdot 4 + 3) (2 + 3)}$

Etapa 2.1.24

Multiplique $2$ por $4$ .

$- \frac{2 \frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 + 3}}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} - \frac{2 ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3))}{(4 + 3) (6 + 3) (8 + 3) (2 + 3)} - \frac{2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3))}{(4 + 3) (6 + 3) (8 + 3) (2 + 3)} - \frac{2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(4 + 3) (6 + 3) (8 + 3) (2 + 3)}$

Etapa 2.2

Combine os numeradores em relação ao denominador comum.

$\frac{- 2 \frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 + 3}}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} + \frac{- 2 ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.3

Cancele o fator comum de $2 + 3$ .

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Etapa 2.3.1

Cancele o fator comum.

Etapa 2.3.2

Divida $((2 \cdot 2 + 3) (2 \cdot 3 + 3)) (2 \cdot 4 + 3)$ por $1$ .

$\frac{- 2 (((2 \cdot 2 + 3) (2 \cdot 3 + 3)) (2 \cdot 4 + 3))}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} + \frac{- 2 ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.4

Multiplique $2$ por $2$ .

$\frac{- 2 ((4 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3))}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} + \frac{- 2 ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.5

Some $4$ e $3$ .

$\frac{- 2 (7 (2 \cdot 3 + 3) (2 \cdot 4 + 3))}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} + \frac{- 2 ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.6

Multiplique $2$ por $3$ .

$\frac{- 2 (7 (6 + 3) (2 \cdot 4 + 3))}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} + \frac{- 2 ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.7

Some $6$ e $3$ .

$\frac{- 2 (7 \cdot 9 (2 \cdot 4 + 3))}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} + \frac{- 2 ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.8

Multiplique $7$ por $9$ .

$\frac{- 2 (63 (2 \cdot 4 + 3))}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} + \frac{- 2 ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.9

Multiplique $2$ por $4$ .

$\frac{- 2 (63 (8 + 3))}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} + \frac{- 2 ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.10

Some $8$ e $3$ .

$\frac{- 2 (63 \cdot 11)}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} + \frac{- 2 ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.11

Multiplique $- 2 (63 \cdot 11)$ .

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Etapa 2.11.1

Multiplique $63$ por $11$ .

$\frac{- 2 \cdot 693}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} + \frac{- 2 ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.11.2

Multiplique $- 2$ por $693$ .

$\frac{- 1386}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} + \frac{- 2 ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.12

Simplifique cada termo.

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Etapa 2.12.1

Some $2$ e $3$ .

$\frac{- 1386}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} + \frac{- 2 (5 (2 \cdot 3 + 3) (2 \cdot 4 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.12.2

Multiplique $2$ por $3$ .

$\frac{- 1386}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} + \frac{- 2 (5 (6 + 3) (2 \cdot 4 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.12.3

Some $6$ e $3$ .

$\frac{- 1386}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} + \frac{- 2 (5 \cdot 9 (2 \cdot 4 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.12.4

Multiplique $5$ por $9$ .

$\frac{- 1386}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} + \frac{- 2 (45 (2 \cdot 4 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.12.5

Multiplique $2$ por $4$ .

$\frac{- 1386}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} + \frac{- 2 (45 (8 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.12.6

Some $8$ e $3$ .

$\frac{- 1386}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} + \frac{- 2 (45 \cdot 11) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.12.7

Multiplique $- 2 (45 \cdot 11)$ .

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Etapa 2.12.7.1

Multiplique $45$ por $11$ .

$\frac{- 1386}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} + \frac{- 2 \cdot 495 - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.12.7.2

Multiplique $- 2$ por $495$ .

$\frac{- 1386}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} + \frac{- 990 - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.12.8

Some $2$ e $3$ .

$\frac{- 1386}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} + \frac{- 990 - 2 (5 (2 \cdot 2 + 3) (2 \cdot 4 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.12.9

Multiplique $2$ por $2$ .

$\frac{- 1386}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} + \frac{- 990 - 2 (5 (4 + 3) (2 \cdot 4 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.12.10

Some $4$ e $3$ .

$\frac{- 1386}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} + \frac{- 990 - 2 (5 \cdot 7 (2 \cdot 4 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.12.11

Multiplique $5$ por $7$ .

$\frac{- 1386}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} + \frac{- 990 - 2 (35 (2 \cdot 4 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.12.12

Multiplique $2$ por $4$ .

$\frac{- 1386}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} + \frac{- 990 - 2 (35 (8 + 3)) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.12.13

Some $8$ e $3$ .

$\frac{- 1386}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} + \frac{- 990 - 2 (35 \cdot 11) - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.12.14

Multiplique $- 2 (35 \cdot 11)$ .

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Etapa 2.12.14.1

Multiplique $35$ por $11$ .

$\frac{- 1386}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} + \frac{- 990 - 2 \cdot 385 - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.12.14.2

Multiplique $- 2$ por $385$ .

$\frac{- 1386}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} + \frac{- 990 - 770 - 2 ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.12.15

Some $2$ e $3$ .

$\frac{- 1386}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} + \frac{- 990 - 770 - 2 (5 (2 \cdot 2 + 3) (2 \cdot 3 + 3))}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.12.16

Multiplique $2$ por $2$ .

$\frac{- 1386}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} + \frac{- 990 - 770 - 2 (5 (4 + 3) (2 \cdot 3 + 3))}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.12.17

Some $4$ e $3$ .

$\frac{- 1386}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} + \frac{- 990 - 770 - 2 (5 \cdot 7 (2 \cdot 3 + 3))}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.12.18

Multiplique $5$ por $7$ .

$\frac{- 1386}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} + \frac{- 990 - 770 - 2 (35 (2 \cdot 3 + 3))}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.12.19

Multiplique $2$ por $3$ .

$\frac{- 1386}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} + \frac{- 990 - 770 - 2 (35 (6 + 3))}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.12.20

Some $6$ e $3$ .

$\frac{- 1386}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} + \frac{- 990 - 770 - 2 (35 \cdot 9)}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.12.21

Multiplique $- 2 (35 \cdot 9)$ .

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Etapa 2.12.21.1

Multiplique $35$ por $9$ .

$\frac{- 1386}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} + \frac{- 990 - 770 - 2 \cdot 315}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.12.21.2

Multiplique $- 2$ por $315$ .

$\frac{- 1386}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} + \frac{- 990 - 770 - 630}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.13

Subtraia $770$ de $- 990$ .

$\frac{- 1386}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} + \frac{- 1760 - 630}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.14

Subtraia $630$ de $- 1760$ .

$\frac{- 1386}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} + \frac{- 2390}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.15

Simplifique cada termo.

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Etapa 2.15.1

Cancele o fator comum de $2 + 3$ .

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Etapa 2.15.1.1

Cancele o fator comum.

$\frac{- 1386}{\frac{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}{2 + 3} (2 + 3)} + \frac{- 2390}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.15.1.2

Divida $((4 + 3) (6 + 3)) (8 + 3)$ por $1$ .

$\frac{- 1386}{((4 + 3) (6 + 3)) (8 + 3) (2 + 3)} + \frac{- 2390}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.15.2

Cancele o fator comum de $- 1386$ e $6 + 3$ .

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Etapa 2.15.2.1

Fatore $3$ de $- 1386$ .

$\frac{3 \cdot - 462}{(4 + 3) (6 + 3) (8 + 3) (2 + 3)} + \frac{- 2390}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.15.2.2

Cancele os fatores comuns.

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Etapa 2.15.2.2.1

Fatore $3$ de $(4 + 3) (6 + 3) (8 + 3) (2 + 3)$ .

$\frac{3 \cdot - 462}{3 ((((4 + 3) (2 + 1)) (8 + 3)) (2 + 3))} + \frac{- 2390}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.15.2.2.2

Cancele o fator comum.

$\frac{3 \cdot - 462}{3 ((((4 + 3) (2 + 1)) (8 + 3)) (2 + 3))} + \frac{- 2390}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.15.2.2.3

Reescreva a expressão.

$\frac{- 462}{(((4 + 3) (2 + 1)) (8 + 3)) (2 + 3)} + \frac{- 2390}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.15.3

Simplifique o denominador.

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Etapa 2.15.3.1

Some $4$ e $3$ .

$\frac{- 462}{7 (2 + 1) (8 + 3) (2 + 3)} + \frac{- 2390}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.15.3.2

Some $2$ e $1$ .

$\frac{- 462}{7 \cdot 3 (8 + 3) (2 + 3)} + \frac{- 2390}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.15.3.3

Multiplique $7$ por $3$ .

$\frac{- 462}{21 (8 + 3) (2 + 3)} + \frac{- 2390}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.15.3.4

Some $8$ e $3$ .

$\frac{- 462}{21 \cdot 11 (2 + 3)} + \frac{- 2390}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.15.3.5

Multiplique $21$ por $11$ .

$\frac{- 462}{231 (2 + 3)} + \frac{- 2390}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.15.3.6

Some $2$ e $3$ .

$\frac{- 462}{231 \cdot 5} + \frac{- 2390}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.15.4

Multiplique $231$ por $5$ .

$\frac{- 462}{1155} + \frac{- 2390}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.15.5

Cancele o fator comum de $- 462$ e $1155$ .

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Etapa 2.15.5.1

Fatore $231$ de $- 462$ .

$\frac{231 (- 2)}{1155} + \frac{- 2390}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.15.5.2

Cancele os fatores comuns.

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Etapa 2.15.5.2.1

Fatore $231$ de $1155$ .

$\frac{231 \cdot - 2}{231 \cdot 5} + \frac{- 2390}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.15.5.2.2

Cancele o fator comum.

$\frac{231 \cdot - 2}{231 \cdot 5} + \frac{- 2390}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.15.5.2.3

Reescreva a expressão.

$\frac{- 2}{5} + \frac{- 2390}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.15.6

Mova o número negativo para a frente da fração.

$- \frac{2}{5} + \frac{- 2390}{(2 + 3) (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.15.7

Simplifique o denominador.

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Etapa 2.15.7.1

Some $2$ e $3$ .

$- \frac{2}{5} + \frac{- 2390}{5 (4 + 3) (6 + 3) (8 + 3)}$

Etapa 2.15.7.2

Some $4$ e $3$ .

$- \frac{2}{5} + \frac{- 2390}{5 \cdot 7 (6 + 3) (8 + 3)}$

Etapa 2.15.7.3

Multiplique $5$ por $7$ .

$- \frac{2}{5} + \frac{- 2390}{35 (6 + 3) (8 + 3)}$

Etapa 2.15.7.4

Some $6$ e $3$ .

$- \frac{2}{5} + \frac{- 2390}{35 \cdot 9 (8 + 3)}$

Etapa 2.15.7.5

Multiplique $35$ por $9$ .

$- \frac{2}{5} + \frac{- 2390}{315 (8 + 3)}$

Etapa 2.15.7.6

Some $8$ e $3$ .

$- \frac{2}{5} + \frac{- 2390}{315 \cdot 11}$

Etapa 2.15.8

Multiplique $315$ por $11$ .

$- \frac{2}{5} + \frac{- 2390}{3465}$

Etapa 2.15.9

Cancele o fator comum de $- 2390$ e $3465$ .

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Etapa 2.15.9.1

Fatore $5$ de $- 2390$ .

$- \frac{2}{5} + \frac{5 (- 478)}{3465}$

Etapa 2.15.9.2

Cancele os fatores comuns.

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Etapa 2.15.9.2.1

Fatore $5$ de $3465$ .

$- \frac{2}{5} + \frac{5 \cdot - 478}{5 \cdot 693}$

Etapa 2.15.9.2.2

Cancele o fator comum.

$- \frac{2}{5} + \frac{5 \cdot - 478}{5 \cdot 693}$

Etapa 2.15.9.2.3

Reescreva a expressão.

$- \frac{2}{5} + \frac{- 478}{693}$

Etapa 2.15.10

Mova o número negativo para a frente da fração.

$- \frac{2}{5} - \frac{478}{693}$

Etapa 2.16

Para escrever $- \frac{2}{5}$ como fração com um denominador comum, multiplique por $\frac{693}{693}$ .

$- \frac{2}{5} \cdot \frac{693}{693} - \frac{478}{693}$

Etapa 2.17

Para escrever $- \frac{478}{693}$ como fração com um denominador comum, multiplique por $\frac{5}{5}$ .

$- \frac{2}{5} \cdot \frac{693}{693} - \frac{478}{693} \cdot \frac{5}{5}$

Etapa 2.18

Escreva cada expressão com um denominador comum de $3465$ , multiplicando cada um por um fator apropriado de $1$ .

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Etapa 2.18.1

Multiplique $\frac{2}{5}$ por $\frac{693}{693}$ .

$- \frac{2 \cdot 693}{5 \cdot 693} - \frac{478}{693} \cdot \frac{5}{5}$

Etapa 2.18.2

Multiplique $5$ por $693$ .

$- \frac{2 \cdot 693}{3465} - \frac{478}{693} \cdot \frac{5}{5}$

Etapa 2.18.3

Multiplique $\frac{478}{693}$ por $\frac{5}{5}$ .

$- \frac{2 \cdot 693}{3465} - \frac{478 \cdot 5}{693 \cdot 5}$

Etapa 2.18.4

Multiplique $693$ por $5$ .

$- \frac{2 \cdot 693}{3465} - \frac{478 \cdot 5}{3465}$

Etapa 2.19

Combine os numeradores em relação ao denominador comum.

$\frac{- 2 \cdot 693 - 478 \cdot 5}{3465}$

Etapa 2.20

Simplifique o numerador.

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Etapa 2.20.1

Multiplique $- 2$ por $693$ .

$\frac{- 1386 - 478 \cdot 5}{3465}$

Etapa 2.20.2

Multiplique $- 478$ por $5$ .

$\frac{- 1386 - 2390}{3465}$

Etapa 2.20.3

Subtraia $2390$ de $- 1386$ .

$\frac{- 3776}{3465}$

Etapa 2.21

Mova o número negativo para a frente da fração.

$- \frac{3776}{3465}$

Etapa 3

O resultado pode ser mostrado de várias formas.

Forma exata:

$- \frac{3776}{3465}$

Forma decimal:

$- 1.08975468 \dots$

Forma de número misto:

$- 1 \frac{311}{3465}$