Simplify (4x-12)/(x^2-9)

$\frac{4 x - 12}{x^{2} - 9}$

Step 1

Factor $4$ out of $4 x - 12$ .

Factor $4$ out of $4 x$ .

$\frac{4 (x) - 12}{x^{2} - 9}$

Factor $4$ out of $- 12$ .

$\frac{4 x + 4 \cdot - 3}{x^{2} - 9}$

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

$\frac{4 (x - 3)}{x^{2} - 9}$

Step 2

Simplify the denominator.

Rewrite $9$ as $3^{2}$ .

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

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 3$ .

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

Step 3

Cancel the common factor of $x - 3$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{4}{x + 3}$