Simplify (x^2-36)/(2x^3-12x^2)

$\frac{x^{2} - 36}{2 x^{3} - 12 x^{2}}$

Simplify the numerator.

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

$\frac{x^{2} - 6^{2}}{2 x^{3} - 12 x^{2}}$

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 $b = 6$ .

$\frac{(x + 6) (x - 6)}{2 x^{3} - 12 x^{2}}$

Simplify terms.

Factor $2 x^{2}$ out of $2 x^{3} - 12 x^{2}$ .

Factor $2 x^{2}$ out of $2 x^{3}$ .

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

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

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

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

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

Cancel the common factor of $x - 6$ .

Cancel the common factor.

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

Rewrite the expression.

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