Answer
(a) $-\frac{2h}{h+1}$
(b) $-\frac{2}{h+1}$
Work Step by Step
We are given: $g(x)=\frac{2}{x+1}$; $x=0$, $x=h$
(a) We calculate the net change:
$g(h)-g(0)=\displaystyle \frac{2}{h+1}-\frac{2}{0+1}=\frac{2}{h+1}-\frac{2(h+1)}{h+1}=-\frac{2h}{h+1}$
(b) We calculate the average rate of change:
$\displaystyle \frac{g(h)-g(0)}{h-0}=\frac{-\frac{2h}{h+1}}{h}=\frac{-2h}{h(h+1)}=-\frac{2}{h+1}$
