Answer
$\frac{1}{\sqrt {4+x}+2}$
Work Step by Step
Multiplying the conjugate of the numerator, we have
$\frac{\sqrt {4+x}-2}{x}=\frac{\sqrt {4+x}-2}{x}\times\frac{\sqrt {4+x}+2}{\sqrt {4+x}+2}=\frac{4+x-4}{x(\sqrt {4+x}+2)}=\frac{1}{\sqrt {4+x}+2}$
