Answer
$f(a)=\frac{1}{a+1}$
$f(a+h)=\frac{1}{a+h+1}$
$\frac{f(a+h)-f(a)}{h}=\frac{-1}{(a+h+1)(a+1)}$
Work Step by Step
We are given $f(x)=\frac{1}{x+1}$
We evaluate:
$f(a)=\frac{1}{a+1}$
$f(a+h)=\frac{1}{a+h+1}$
$\frac{f(a+h)-f(a)}{h}=\frac{\frac{1}{a+h+1}-\frac{1}{a+1}}{h}=\frac{a+1-a-h-1}{(a+h+1)(a+1)h}=\frac{-1}{(a+h+1)(a+1)}$