Answer
$\frac{1}{\sqrt {x+h+1}+\sqrt {x+1}} $
Work Step by Step
Step 1. $f(x+h)=\sqrt {x+h+1}$
Step 2. $f(x+h)-f(x)=\sqrt {x+h+1}-\sqrt {x+1}$
Step 3. $\frac{f(x+h)-f(x)}{h}=\frac{\sqrt {x+h+1}-\sqrt {x+1}}{h}=\frac{\sqrt {x+h+1}-\sqrt {x+1}}{h}\times\frac{\sqrt {x+h+1}+\sqrt {x+1}}{\sqrt {x+h+1}+\sqrt {x+1}}=\frac{1}{\sqrt {x+h+1}+\sqrt {x+1}} $
