#### Answer

$\frac{x^2+7x-20}{(x+2)(x-4)}$

#### Work Step by Step

$\frac{5}{2+x}+\frac{x}{x-4}$
$=\frac{5(x-4)}{(x+2)(x-4)}+\frac{x(x+2)}{(x-4)(x+2)}$
$=\frac{5x-20}{(x+2)(x-4)}+\frac{x^2+2x}{(x-4)(x+2)}$
$=\frac{5x-20+x^2+2x}{(x+2)(x-4)}$
$=\frac{x^2+7x-20}{(x+2)(x-4)}$