Answer
Domain: All real numbers; $x \ne \pm 3$
Work Step by Step
The domain of the function is all real numbers, except for when the denominator is 0. Thus, we let the denominator equal 0:
$$ 4(x^2-9) =0 \\ 4x^2 -36 =0 \\ x^2 =9 \\ x= \pm 3 $$
Thus, we know that x cannot equal 3 or -3.
Domain: All real numbers; $x \ne \pm 3 $
