Simplify 7/(2(x+6)^2-4(x+6))

$\frac{7}{2 {(x + 6)}^{2} - 4 (x + 6)}$

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

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

$\frac{7}{2 (x + 6) (x + 6) - 4 (x + 6)}$

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

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

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

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

Subtract $2$ from $6$ .

$\frac{7}{2 (x + 6) (x + 4)}$