Simplify (2x^2-12x)/(x^2-36)

$\frac{2 x^{2} - 12 x}{x^{2} - 36}$

Factor $2 x$ out of $2 x^{2} - 12 x$ .

Factor $2 x$ out of $2 x^{2}$ .

$\frac{2 x (x) - 12 x}{x^{2} - 36}$

Factor $2 x$ out of $- 12 x$ .

$\frac{2 x (x) + 2 x (- 6)}{x^{2} - 36}$

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

$\frac{2 x (x - 6)}{x^{2} - 36}$

Simplify the denominator.

Rewrite $36$ as $6^{2}$ .

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

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 $b = 6$ .

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

Cancel the common factor of $x - 6$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{2 x}{x + 6}$