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

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

Step 1

Simplify the denominator.

Rewrite $4$ as $2^{2}$ .

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

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 $b = 2$ .

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

Step 2

Cancel the common factor of $x - 2$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{x + 2}$