Simplify (x-6)/(x^2-36)

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

Step 1

Simplify the denominator.

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

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

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 $b = 6$ .

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

Step 2

Cancel the common factor of $x - 6$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{x + 6}$