Answer
$\displaystyle\frac{1}{\sqrt{x+h}+\sqrt{x}}$
Work Step by Step
We multiply the numerator and denominator by the conjugate $\sqrt{x+h}+\sqrt{x}$ and use $(a-b)(a+b)=a^2-b^2$ to simplify:
$\displaystyle \frac{\sqrt{x+h}-\sqrt{x}}{h}=\frac{\sqrt{x+h}-\sqrt{x}}{h}*\frac{\sqrt{x+h}+\sqrt{x}}{\sqrt{x+h}+\sqrt{x}}=\frac{x+h-x}{h(\sqrt{x+h}+\sqrt{x})}=\frac{h}{h(\sqrt{x+h}+\sqrt{x})}=\frac{1}{\sqrt{x+h}+\sqrt{x}}$
