Cálculo Ejemplos

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

Paso 1

Expande la serie para cada valor de $j$ .

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

Paso 2

Simplifica.

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Paso 2.1

Obtén el denominador común

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Paso 2.1.1

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

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

Paso 2.1.2

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

Paso 2.1.3

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

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

Paso 2.1.4

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

Paso 2.1.5

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

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

Paso 2.1.6

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

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

Paso 2.1.7

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

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

Paso 2.1.8

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

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

Paso 2.1.9

Reordena los factores de $(2 + 3) \frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 + 3}$ .

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

Paso 2.1.10

Multiplica $2$ por $2$ .

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

Paso 2.1.11

Multiplica $2$ por $3$ .

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

Paso 2.1.12

Multiplica $2$ por $4$ .

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

Paso 2.1.13

Reordena los factores de $(2 \cdot 2 + 3) ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3))$ .

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

Paso 2.1.14

Multiplica $2$ por $2$ .

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

Paso 2.1.15

Multiplica $2$ por $3$ .

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

Paso 2.1.16

Multiplica $2$ por $4$ .

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

Paso 2.1.17

Reordena los factores de $(2 \cdot 3 + 3) ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3))$ .

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

Paso 2.1.18

Multiplica $2$ por $2$ .

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

Paso 2.1.19

Multiplica $2$ por $3$ .

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

Paso 2.1.20

Multiplica $2$ por $4$ .

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

Paso 2.1.21

Reordena los factores de $(2 \cdot 4 + 3) ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))$ .

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

Paso 2.1.22

Multiplica $2$ por $2$ .

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

Paso 2.1.23

Multiplica $2$ por $3$ .

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

Paso 2.1.24

Multiplica $2$ por $4$ .

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

Paso 2.2

Combina los numeradores sobre el denominador común.

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

Paso 2.3

Cancela el factor común de $2 + 3$ .

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Paso 2.3.1

Cancela el factor común.

Paso 2.3.2

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

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

Paso 2.4

Multiplica $2$ por $2$ .

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

Paso 2.5

Suma $4$ y $3$ .

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

Paso 2.6

Multiplica $2$ por $3$ .

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

Paso 2.7

Suma $6$ y $3$ .

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

Paso 2.8

Multiplica $7$ por $9$ .

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

Paso 2.9

Multiplica $2$ por $4$ .

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

Paso 2.10

Suma $8$ y $3$ .

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

Paso 2.11

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

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Paso 2.11.1

Multiplica $63$ por $11$ .

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

Paso 2.11.2

Multiplica $- 2$ por $693$ .

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

Paso 2.12

Simplifica cada término.

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Paso 2.12.1

Suma $2$ y $3$ .

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

Paso 2.12.2

Multiplica $2$ por $3$ .

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

Paso 2.12.3

Suma $6$ y $3$ .

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

Paso 2.12.4

Multiplica $5$ por $9$ .

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

Paso 2.12.5

Multiplica $2$ por $4$ .

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

Paso 2.12.6

Suma $8$ y $3$ .

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

Paso 2.12.7

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

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Paso 2.12.7.1

Multiplica $45$ por $11$ .

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

Paso 2.12.7.2

Multiplica $- 2$ por $495$ .

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

Paso 2.12.8

Suma $2$ y $3$ .

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

Paso 2.12.9

Multiplica $2$ por $2$ .

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

Paso 2.12.10

Suma $4$ y $3$ .

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

Paso 2.12.11

Multiplica $5$ por $7$ .

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

Paso 2.12.12

Multiplica $2$ por $4$ .

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

Paso 2.12.13

Suma $8$ y $3$ .

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

Paso 2.12.14

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

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Paso 2.12.14.1

Multiplica $35$ por $11$ .

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

Paso 2.12.14.2

Multiplica $- 2$ por $385$ .

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

Paso 2.12.15

Suma $2$ y $3$ .

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

Paso 2.12.16

Multiplica $2$ por $2$ .

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

Paso 2.12.17

Suma $4$ y $3$ .

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

Paso 2.12.18

Multiplica $5$ por $7$ .

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

Paso 2.12.19

Multiplica $2$ por $3$ .

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

Paso 2.12.20

Suma $6$ y $3$ .

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

Paso 2.12.21

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

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Paso 2.12.21.1

Multiplica $35$ por $9$ .

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

Paso 2.12.21.2

Multiplica $- 2$ por $315$ .

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

Paso 2.13

Resta $770$ de $- 990$ .

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

Paso 2.14

Resta $630$ de $- 1760$ .

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

Paso 2.15

Simplifica cada término.

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Paso 2.15.1

Cancela el factor común de $2 + 3$ .

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Paso 2.15.1.1

Cancela el factor común.

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

Paso 2.15.1.2

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

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

Paso 2.15.2

Cancela el factor común de $- 1386$ y $6 + 3$ .

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Paso 2.15.2.1

Factoriza $3$ de $- 1386$ .

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

Paso 2.15.2.2

Cancela los factores comunes.

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Paso 2.15.2.2.1

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

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

Paso 2.15.2.2.2

Cancela el factor común.

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

Paso 2.15.2.2.3

Reescribe la expresión.

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

Paso 2.15.3

Simplifica el denominador.

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Paso 2.15.3.1

Suma $4$ y $3$ .

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

Paso 2.15.3.2

Suma $2$ y $1$ .

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

Paso 2.15.3.3

Multiplica $7$ por $3$ .

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

Paso 2.15.3.4

Suma $8$ y $3$ .

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

Paso 2.15.3.5

Multiplica $21$ por $11$ .

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

Paso 2.15.3.6

Suma $2$ y $3$ .

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

Paso 2.15.4

Multiplica $231$ por $5$ .

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

Paso 2.15.5

Cancela el factor común de $- 462$ y $1155$ .

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Paso 2.15.5.1

Factoriza $231$ de $- 462$ .

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

Paso 2.15.5.2

Cancela los factores comunes.

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Paso 2.15.5.2.1

Factoriza $231$ de $1155$ .

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

Paso 2.15.5.2.2

Cancela el factor común.

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

Paso 2.15.5.2.3

Reescribe la expresión.

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

Paso 2.15.6

Mueve el negativo al frente de la fracción.

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

Paso 2.15.7

Simplifica el denominador.

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Paso 2.15.7.1

Suma $2$ y $3$ .

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

Paso 2.15.7.2

Suma $4$ y $3$ .

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

Paso 2.15.7.3

Multiplica $5$ por $7$ .

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

Paso 2.15.7.4

Suma $6$ y $3$ .

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

Paso 2.15.7.5

Multiplica $35$ por $9$ .

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

Paso 2.15.7.6

Suma $8$ y $3$ .

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

Paso 2.15.8

Multiplica $315$ por $11$ .

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

Paso 2.15.9

Cancela el factor común de $- 2390$ y $3465$ .

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Paso 2.15.9.1

Factoriza $5$ de $- 2390$ .

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

Paso 2.15.9.2

Cancela los factores comunes.

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Paso 2.15.9.2.1

Factoriza $5$ de $3465$ .

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

Paso 2.15.9.2.2

Cancela el factor común.

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

Paso 2.15.9.2.3

Reescribe la expresión.

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

Paso 2.15.10

Mueve el negativo al frente de la fracción.

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

Paso 2.16

Para escribir $- \frac{2}{5}$ como una fracción con un denominador común, multiplica por $\frac{693}{693}$ .

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

Paso 2.17

Para escribir $- \frac{478}{693}$ como una fracción con un denominador común, multiplica por $\frac{5}{5}$ .

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

Paso 2.18

Escribe cada expresión con un denominador común de $3465$ , mediante la multiplicación de cada uno por un factor adecuado de $1$ .

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Paso 2.18.1

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

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

Paso 2.18.2

Multiplica $5$ por $693$ .

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

Paso 2.18.3

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

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

Paso 2.18.4

Multiplica $693$ por $5$ .

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

Paso 2.19

Combina los numeradores sobre el denominador común.

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

Paso 2.20

Simplifica el numerador.

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Paso 2.20.1

Multiplica $- 2$ por $693$ .

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

Paso 2.20.2

Multiplica $- 478$ por $5$ .

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

Paso 2.20.3

Resta $2390$ de $- 1386$ .

$\frac{- 3776}{3465}$

Paso 2.21

Mueve el negativo al frente de la fracción.

$- \frac{3776}{3465}$

Paso 3

El resultado puede mostrarse de distintas formas.

Forma exacta:

$- \frac{3776}{3465}$

Forma decimal:

$- 1.08975468 \dots$

Forma de número mixto:

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