Simplify (-8u^2-8u+29)/(-3u+7)+(-8u^2+7u-6)/(3u-7)

$\frac{- 8 u^{2} - 8 u + 29}{- 3 u + 7} + \frac{- 8 u^{2} + 7 u - 6}{3 u - 7}$

Step 1

Simplify terms.

Factor $- 1$ out of $3 u$ .

$\frac{- 8 u^{2} - 8 u + 29}{- 3 u + 7} + \frac{- 8 u^{2} + 7 u - 6}{- (- 3 u) - 7}$

Rewrite $- 7$ as $- 1 (7)$ .

$\frac{- 8 u^{2} - 8 u + 29}{- 3 u + 7} + \frac{- 8 u^{2} + 7 u - 6}{- (- 3 u) - 1 (7)}$

Factor $- 1$ out of $- (- 3 u) - 1 (7)$ .

$\frac{- 8 u^{2} - 8 u + 29}{- 3 u + 7} + \frac{- 8 u^{2} + 7 u - 6}{- (- 3 u + 7)}$

Move a negative from the denominator of $\frac{- 8 u^{2} + 7 u - 6}{- (- 3 u + 7)}$ to the numerator.

$\frac{- 8 u^{2} - 8 u + 29}{- 3 u + 7} + \frac{- (- 8 u^{2} + 7 u - 6)}{- 3 u + 7}$

Combine the numerators over the common denominator.

$\frac{- 8 u^{2} - 8 u + 29 - (- 8 u^{2} + 7 u - 6)}{- 3 u + 7}$

Step 2

Simplify the numerator.

Apply the distributive property.

$\frac{- 8 u^{2} - 8 u + 29 - (- 8 u^{2}) - (7 u) - - 6}{- 3 u + 7}$

Simplify.

Multiply $- 8$ by $- 1$ .

$\frac{- 8 u^{2} - 8 u + 29 + 8 u^{2} - (7 u) - - 6}{- 3 u + 7}$

Multiply $7$ by $- 1$ .

$\frac{- 8 u^{2} - 8 u + 29 + 8 u^{2} - 7 u - - 6}{- 3 u + 7}$

Multiply $- 1$ by $- 6$ .

$\frac{- 8 u^{2} - 8 u + 29 + 8 u^{2} - 7 u + 6}{- 3 u + 7}$

Add $- 8 u^{2}$ and $8 u^{2}$ .

$\frac{- 8 u + 29 + 0 - 7 u + 6}{- 3 u + 7}$

Add $- 8 u$ and $0$ .

$\frac{- 8 u + 29 - 7 u + 6}{- 3 u + 7}$

Subtract $7 u$ from $- 8 u$ .

$\frac{- 15 u + 29 + 6}{- 3 u + 7}$

Add $29$ and $6$ .

$\frac{- 15 u + 35}{- 3 u + 7}$

Factor $5$ out of $- 15 u + 35$ .

Factor $5$ out of $- 15 u$ .

$\frac{5 (- 3 u) + 35}{- 3 u + 7}$

Factor $5$ out of $35$ .

$\frac{5 (- 3 u) + 5 (7)}{- 3 u + 7}$

Factor $5$ out of $5 (- 3 u) + 5 (7)$ .

$\frac{5 (- 3 u + 7)}{- 3 u + 7}$

Step 3

Cancel the common factor of $- 3 u + 7$ .

Cancel the common factor.

$\frac{5 (- 3 u + 7)}{- 3 u + 7}$

Divide $5$ by $1$ .

$5$