Calculus Examples

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

Step 1

Expand the series for each value of $j$ .

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

Step 2

Simplify.

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Step 2.1

Find the common denominator.

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Step 2.1.1

Multiply $\frac{2}{2 \cdot 1 + 3}$ by $\frac{\frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 \cdot 1 + 3}}{\frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 \cdot 1 + 3}}$ .

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

Step 2.1.2

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

Step 2.1.3

Multiply $\frac{2}{2 \cdot 2 + 3}$ by $\frac{(2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{(2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}$ .

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

Step 2.1.4

Multiply $\frac{2}{2 \cdot 2 + 3}$ by $\frac{(2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{(2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}$ .

Step 2.1.5

Multiply $\frac{2}{2 \cdot 3 + 3}$ by $\frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3)}{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3)}$ .

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

Step 2.1.6

Multiply $\frac{2}{2 \cdot 3 + 3}$ by $\frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3)}{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3)}$ .

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

Step 2.1.7

Multiply $\frac{2}{2 \cdot 4 + 3}$ by $\frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3)}{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3)}$ .

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

Step 2.1.8

Multiply $\frac{2}{2 \cdot 4 + 3}$ by $\frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3)}{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3)}$ .

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

Step 2.1.9

Reorder the factors of $(2 + 3) \frac{(2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3)}{2 + 3}$ .

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

Step 2.1.10

Multiply $2$ by $2$ .

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

Step 2.1.11

Multiply $2$ by $3$ .

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

Step 2.1.12

Multiply $2$ by $4$ .

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

Step 2.1.13

Reorder the factors of $(2 \cdot 2 + 3) ((2 + 3) (2 \cdot 3 + 3) (2 \cdot 4 + 3))$ .

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

Step 2.1.14

Multiply $2$ by $2$ .

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

Step 2.1.15

Multiply $2$ by $3$ .

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

Step 2.1.16

Multiply $2$ by $4$ .

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

Step 2.1.17

Reorder the factors of $(2 \cdot 3 + 3) ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 4 + 3))$ .

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

Step 2.1.18

Multiply $2$ by $2$ .

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

Step 2.1.19

Multiply $2$ by $3$ .

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

Step 2.1.20

Multiply $2$ by $4$ .

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

Step 2.1.21

Reorder the factors of $(2 \cdot 4 + 3) ((2 + 3) (2 \cdot 2 + 3) (2 \cdot 3 + 3))$ .

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

Step 2.1.22

Multiply $2$ by $2$ .

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

Step 2.1.23

Multiply $2$ by $3$ .

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

Step 2.1.24

Multiply $2$ by $4$ .

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

Step 2.2

Combine the numerators over the common denominator.

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

Step 2.3

Cancel the common factor of $2 + 3$ .

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Step 2.3.1

Cancel the common factor.

Step 2.3.2

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

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

Step 2.4

Multiply $2$ by $2$ .

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

Step 2.5

Add $4$ and $3$ .

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

Step 2.6

Multiply $2$ by $3$ .

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

Step 2.7

Add $6$ and $3$ .

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

Step 2.8

Multiply $7$ by $9$ .

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

Step 2.9

Multiply $2$ by $4$ .

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

Step 2.10

Add $8$ and $3$ .

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

Step 2.11

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

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Step 2.11.1

Multiply $63$ by $11$ .

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

Step 2.11.2

Multiply $- 2$ by $693$ .

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

Step 2.12

Simplify each term.

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Step 2.12.1

Add $2$ and $3$ .

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

Step 2.12.2

Multiply $2$ by $3$ .

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

Step 2.12.3

Add $6$ and $3$ .

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

Step 2.12.4

Multiply $5$ by $9$ .

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

Step 2.12.5

Multiply $2$ by $4$ .

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

Step 2.12.6

Add $8$ and $3$ .

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

Step 2.12.7

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

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Step 2.12.7.1

Multiply $45$ by $11$ .

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

Step 2.12.7.2

Multiply $- 2$ by $495$ .

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

Step 2.12.8

Add $2$ and $3$ .

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

Step 2.12.9

Multiply $2$ by $2$ .

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

Step 2.12.10

Add $4$ and $3$ .

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

Step 2.12.11

Multiply $5$ by $7$ .

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

Step 2.12.12

Multiply $2$ by $4$ .

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

Step 2.12.13

Add $8$ and $3$ .

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

Step 2.12.14

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

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Step 2.12.14.1

Multiply $35$ by $11$ .

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

Step 2.12.14.2

Multiply $- 2$ by $385$ .

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

Step 2.12.15

Add $2$ and $3$ .

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

Step 2.12.16

Multiply $2$ by $2$ .

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

Step 2.12.17

Add $4$ and $3$ .

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

Step 2.12.18

Multiply $5$ by $7$ .

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

Step 2.12.19

Multiply $2$ by $3$ .

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

Step 2.12.20

Add $6$ and $3$ .

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

Step 2.12.21

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

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Step 2.12.21.1

Multiply $35$ by $9$ .

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

Step 2.12.21.2

Multiply $- 2$ by $315$ .

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

Step 2.13

Subtract $770$ from $- 990$ .

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

Step 2.14

Subtract $630$ from $- 1760$ .

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

Step 2.15

Simplify each term.

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Step 2.15.1

Cancel the common factor of $2 + 3$ .

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Step 2.15.1.1

Cancel the common factor.

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

Step 2.15.1.2

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

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

Step 2.15.2

Cancel the common factor of $- 1386$ and $6 + 3$ .

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Step 2.15.2.1

Factor $3$ out of $- 1386$ .

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

Step 2.15.2.2

Cancel the common factors.

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Step 2.15.2.2.1

Factor $3$ out of $(4 + 3) (6 + 3) (8 + 3) (2 + 3)$ .

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

Step 2.15.2.2.2

Cancel the common factor.

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

Step 2.15.2.2.3

Rewrite the expression.

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

Step 2.15.3

Simplify the denominator.

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Step 2.15.3.1

Add $4$ and $3$ .

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

Step 2.15.3.2

Add $2$ and $1$ .

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

Step 2.15.3.3

Multiply $7$ by $3$ .

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

Step 2.15.3.4

Add $8$ and $3$ .

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

Step 2.15.3.5

Multiply $21$ by $11$ .

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

Step 2.15.3.6

Add $2$ and $3$ .

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

Step 2.15.4

Multiply $231$ by $5$ .

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

Step 2.15.5

Cancel the common factor of $- 462$ and $1155$ .

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Step 2.15.5.1

Factor $231$ out of $- 462$ .

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

Step 2.15.5.2

Cancel the common factors.

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Step 2.15.5.2.1

Factor $231$ out of $1155$ .

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

Step 2.15.5.2.2

Cancel the common factor.

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

Step 2.15.5.2.3

Rewrite the expression.

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

Step 2.15.6

Move the negative in front of the fraction.

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

Step 2.15.7

Simplify the denominator.

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Step 2.15.7.1

Add $2$ and $3$ .

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

Step 2.15.7.2

Add $4$ and $3$ .

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

Step 2.15.7.3

Multiply $5$ by $7$ .

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

Step 2.15.7.4

Add $6$ and $3$ .

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

Step 2.15.7.5

Multiply $35$ by $9$ .

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

Step 2.15.7.6

Add $8$ and $3$ .

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

Step 2.15.8

Multiply $315$ by $11$ .

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

Step 2.15.9

Cancel the common factor of $- 2390$ and $3465$ .

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Step 2.15.9.1

Factor $5$ out of $- 2390$ .

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

Step 2.15.9.2

Cancel the common factors.

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Step 2.15.9.2.1

Factor $5$ out of $3465$ .

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

Step 2.15.9.2.2

Cancel the common factor.

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

Step 2.15.9.2.3

Rewrite the expression.

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

Step 2.15.10

Move the negative in front of the fraction.

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

Step 2.16

To write $- \frac{2}{5}$ as a fraction with a common denominator, multiply by $\frac{693}{693}$ .

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

Step 2.17

To write $- \frac{478}{693}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 2.18

Write each expression with a common denominator of $3465$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.18.1

Multiply $\frac{2}{5}$ by $\frac{693}{693}$ .

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

Step 2.18.2

Multiply $5$ by $693$ .

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

Step 2.18.3

Multiply $\frac{478}{693}$ by $\frac{5}{5}$ .

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

Step 2.18.4

Multiply $693$ by $5$ .

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

Step 2.19

Combine the numerators over the common denominator.

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

Step 2.20

Simplify the numerator.

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Step 2.20.1

Multiply $- 2$ by $693$ .

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

Step 2.20.2

Multiply $- 478$ by $5$ .

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

Step 2.20.3

Subtract $2390$ from $- 1386$ .

$\frac{- 3776}{3465}$

Step 2.21

Move the negative in front of the fraction.

$- \frac{3776}{3465}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \frac{3776}{3465}$

Decimal Form:

$- 1.08975468 \dots$

Mixed Number Form:

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