Simplify ( square root of x+2)/(x^2-4)

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

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

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

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 $b = 2$ .

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