#### Answer

$[-2, 3) \cup (3,\ \infty)$

#### Work Step by Step

We are given:
$g(x)= \frac{\sqrt{2+x}}{3-x}$
The domain of a function consists of all values that $x$ is allowed to have. In this case, we can not take the square root of a negative number, so:
$2+x\geq 0$
$ x\geq-2$
We also can not have division by $0$:
$3-x\neq 0$
$ x\neq 3$
Therefore, the domain is: $[-2, 3) \cup (3,\ \infty)$