Answer
The domain is {$x|x\gt9$}.
Work Step by Step
Requirement (1)
For a square root to be defined, the expression inside the radial sign must be greater than or equal to $0$.
The domain is defined by applying the requirement:
$x-9\geq0$
$x-9+9\ge 0+9$
$x\geq 9$
Requirement (2)
For a fraction to be defined, the denominator can not be equal to $0$.
Thus,
$\sqrt{x-9}\ne0$
$(\sqrt{x-9})^2\ne 0^2$
$x-9\ne0$
$x-9+9\ne0+9$
$x\ne9$
The two requirements can be applied together, to define the domain:
$x\geq9$ and $x\ne9$.
Therefore, the domain is {$x|x\gt9$}.
