Simplify f(x)=(x^2-4)/(x+2)

$f (x) = \frac{x^{2} - 4}{x + 2}$

Simplify the numerator.

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

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

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 $b = 2$ .

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

Cancel the common factor of $x + 2$ .

Cancel the common factor.

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

Divide $x - 2$ by $1$ .

$f (x) = x - 2$