Answer
$\displaystyle\frac{x(\sqrt{x}-2)}{x-4}$
Work Step by Step
We multiply the numerator and denominator by $2-\sqrt{x}$ and use the fact that $(a-b)(a+b)=a^2-b^2$ to simplify:
$\displaystyle \frac{x}{2+\sqrt{x}}=\frac{x}{2+\sqrt{x}}*\frac{2-\sqrt{x}}{2-\sqrt{x}}=\frac{2x-x\sqrt{x}}{2^{2}-(\sqrt{x})^{2}}=\frac{x(2-\sqrt{x})}{4-x}=\frac{x(\sqrt{x}-2)}{x-4}$
