Evaluate 7/(3(x+5)^2-2(x+5))

$\frac{7}{3 {(x + 5)}^{2} - 2 (x + 5)}$

Step 1

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

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

$\frac{7}{(x + 5) (3 (x + 5)) - 2 (x + 5)}$

Factor $x + 5$ out of $- 2 (x + 5)$ .

$\frac{7}{(x + 5) (3 (x + 5)) + (x + 5) \cdot - 2}$

Factor $x + 5$ out of $(x + 5) (3 (x + 5)) + (x + 5) \cdot - 2$ .

$\frac{7}{(x + 5) (3 (x + 5) - 2)}$

Step 2

Apply the distributive property.

$\frac{7}{(x + 5) (3 x + 3 \cdot 5 - 2)}$

Step 3

Multiply $3$ by $5$ .

$\frac{7}{(x + 5) (3 x + 15 - 2)}$

Step 4

Subtract $2$ from $15$ .

$\frac{7}{(x + 5) (3 x + 13)}$