Answer
The domain is $\{z|z\geq-3, z\ne2\}$.
Work Step by Step
Requirement (1)
For a fraction to be defined, the denominator can not be equal to $0$.
Thus,
$z-2\ne0$
$z-2+2\ne0+2$
$z\ne2$
Requirement (2)
For a square root to be defined, the expression inside the radical sign must be greater than or equal to $0$.
Thus,
$z+3\geq0$
$z+3-3\ge 0-3$
$z\geq-3$
The two requirements can be applied together, to define the domain:
$$z\ne2\text{ and } z\geq-3$$
Therefore the domain is $\{z|z\geq-3, z\ne2\}$.
