Simplify 9/(-6(x+2)^2+7(x+2))

$\frac{9}{- 6 {(x + 2)}^{2} + 7 (x + 2)}$

Step 1

Simplify the denominator.

Factor $x + 2$ out of $- 6 {(x + 2)}^{2} + 7 (x + 2)$ .

Factor $x + 2$ out of $- 6 {(x + 2)}^{2}$ .

$\frac{9}{(x + 2) (- 6 (x + 2)) + 7 (x + 2)}$

Factor $x + 2$ out of $7 (x + 2)$ .

$\frac{9}{(x + 2) (- 6 (x + 2)) + (x + 2) \cdot 7}$

Factor $x + 2$ out of $(x + 2) (- 6 (x + 2)) + (x + 2) \cdot 7$ .

$\frac{9}{(x + 2) (- 6 (x + 2) + 7)}$

Apply the distributive property.

$\frac{9}{(x + 2) (- 6 x - 6 \cdot 2 + 7)}$

Multiply $- 6$ by $2$ .

$\frac{9}{(x + 2) (- 6 x - 12 + 7)}$

Add $- 12$ and $7$ .

$\frac{9}{(x + 2) (- 6 x - 5)}$

Step 2

Simplify with factoring out.

Factor $- 1$ out of $- 6 x$ .

$\frac{9}{(x + 2) (- (6 x) - 5)}$

Rewrite $- 5$ as $- 1 (5)$ .

$\frac{9}{(x + 2) (- (6 x) - 1 (5))}$

Factor $- 1$ out of $- (6 x) - 1 (5)$ .

$\frac{9}{(x + 2) (- (6 x + 5))}$

Rewrite negatives.

Rewrite $- (6 x + 5)$ as $- 1 (6 x + 5)$ .

$\frac{9}{(x + 2) (- 1 (6 x + 5))}$

Move the negative in front of the fraction.

$- \frac{9}{(x + 2) (6 x + 5)}$