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