Evaluate 8/(-4(x+3)^2+5(x+3))

$\frac{8}{- 4 {(x + 3)}^{2} + 5 (x + 3)}$

Simplify the denominator.

Factor $x + 3$ out of $- 4 {(x + 3)}^{2} + 5 (x + 3)$ .

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

$\frac{8}{(x + 3) (- 4 (x + 3)) + 5 (x + 3)}$

Factor $x + 3$ out of $5 (x + 3)$ .

$\frac{8}{(x + 3) (- 4 (x + 3)) + (x + 3) \cdot 5}$

Factor $x + 3$ out of $(x + 3) (- 4 (x + 3)) + (x + 3) \cdot 5$ .

$\frac{8}{(x + 3) (- 4 (x + 3) + 5)}$

Apply the distributive property.

$\frac{8}{(x + 3) (- 4 x - 4 \cdot 3 + 5)}$

Multiply $- 4$ by $3$ .

$\frac{8}{(x + 3) (- 4 x - 12 + 5)}$

Add $- 12$ and $5$ .

$\frac{8}{(x + 3) (- 4 x - 7)}$

Simplify with factoring out.

Factor $- 1$ out of $- 4 x$ .

$\frac{8}{(x + 3) (- (4 x) - 7)}$

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

$\frac{8}{(x + 3) (- (4 x) - 1 (7))}$

Factor $- 1$ out of $- (4 x) - 1 (7)$ .

$\frac{8}{(x + 3) (- (4 x + 7))}$

Rewrite negatives.

Rewrite $- (4 x + 7)$ as $- 1 (4 x + 7)$ .

$\frac{8}{(x + 3) (- 1 (4 x + 7))}$

Move the negative in front of the fraction.

$- \frac{8}{(x + 3) (4 x + 7)}$