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

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

Step 1

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

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

Step 2

Apply the distributive property.

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

Step 3

Multiply $6$ by $2$ .

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

Step 4

Subtract $7$ from $12$ .

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