Answer
$\displaystyle \frac{1}{\sqrt{x+h+1}+\sqrt{x+1}}$
Work Step by Step
... We will use the hint of the previous exercise, as f(x) has similar form
$f(x)=\sqrt{x+1}$
$\displaystyle \frac{f(x+h)-f(x)}{h}=\frac{\sqrt{x+h+1}-\sqrt{x+1}}{h}$
... use the hint, rationalize with $\displaystyle \frac{\sqrt{x+h+1}+\sqrt{x+1}}{\sqrt{x+h+1}+\sqrt{x+1}}$
$=\displaystyle \frac{(x+h+1)-(x+1)}{h(\sqrt{x+h+1}+\sqrt{x+1})}$
$=\displaystyle \frac{h}{h(\sqrt{x+h+1}+\sqrt{x+1})}$ ... h cancels
$=\displaystyle \frac{1}{\sqrt{x+h+1}+\sqrt{x+1}}$