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