#### Answer

$g(-2)=0$
$g(2)=$ undefined
$g(0)=-1$
$g(a)=\frac{a+2}{a-2}$
$g(a^{2}-2)=\frac{a^{2}}{a^{2}-4}$
$g(a+1)=\frac{a+3}{a-1}$

#### Work Step by Step

We are given:
$g(t)= \frac{t+2}{t-2}$
We evaluate:
$g(-2)=\frac{-2+2}{-2-2}=0$
$g(2)=\frac{2+2}{2-2}=\frac{4}{0}$= undefined
$g(0)= \frac{0+2}{0-2}=\frac{2}{-2}=-1$
$g(a)=\frac{a+2}{a-2}$
$g(a^{2}-2)= \frac{a^{2}-2+2}{a^{2}-2-2}=\frac{a^{2}}{a^{2}-4}$
$g(a+1)=\frac{a+1+2}{a+1-2}=\frac{a+3}{a-1}$