Simplify 5/(-2(x+4)^2+6(x+4))

$\frac{5}{- 2 {(x + 4)}^{2} + 6 (x + 4)}$

Simplify the denominator.

Factor $2 (x + 4)$ out of $- 2 {(x + 4)}^{2} + 6 (x + 4)$ .

Factor $2 (x + 4)$ out of $- 2 {(x + 4)}^{2}$ .

$\frac{5}{2 (x + 4) (- (x + 4)) + 6 (x + 4)}$

Factor $2 (x + 4)$ out of $6 (x + 4)$ .

$\frac{5}{2 (x + 4) (- (x + 4)) + 2 (x + 4) (3)}$

Factor $2 (x + 4)$ out of $2 (x + 4) (- (x + 4)) + 2 (x + 4) (3)$ .

$\frac{5}{2 (x + 4) (- (x + 4) + 3)}$

Apply the distributive property.

$\frac{5}{2 (x + 4) (- x - 1 \cdot 4 + 3)}$

Multiply $- 1$ by $4$ .

$\frac{5}{2 (x + 4) (- x - 4 + 3)}$

Add $- 4$ and $3$ .

$\frac{5}{2 (x + 4) (- x - 1)}$

Simplify with factoring out.

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

$\frac{5}{2 (x + 4) (- (x) - 1)}$

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

$\frac{5}{2 (x + 4) (- (x) - 1 (1))}$

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

$\frac{5}{2 (x + 4) (- (x + 1))}$

Rewrite negatives.

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

$\frac{5}{2 (x + 4) (- 1 (x + 1))}$

Move the negative in front of the fraction.

$- \frac{5}{(2 (x + 4)) (x + 1)}$