Answer
$(a)$
Work Step by Step
The domain of a rational expression is the whole set of real numbers, excluding the numbers that make the denominator equal to zero (since division of zero is not allowed).
Here, we exclude $x$ for which the denominator is equal to zero.
To find the numbers that will make the denominator zero, set the denominator equal to zero then solve the equation:
$ x^{2}-9=0\qquad$
$x^{2}-9+9=0+9$
Take the square root of both sides:
$\sqrt{x^2}=\pm \sqrt{9}$
$x=\pm 3$
Thus, $x$ cannot be $3$ or $-3$.
The answer is choice $(a)$.