Answer
$\frac{1}{(\sqrt{x+2}+\sqrt x)}$
Work Step by Step
$\frac{\sqrt{x+2}-\sqrt x}{2}=\frac{(\sqrt{x+2}-\sqrt x)(\sqrt{x+2}+\sqrt x)}{2(\sqrt{x+2}+\sqrt x)}=\frac{x+2-x}{2(\sqrt{x+2}+\sqrt x)}=\frac{2}{2(\sqrt{x+2}+\sqrt x)}=\frac{1}{(\sqrt{x+2}+\sqrt x)}$
