Answer
$(a)$
Work Step by Step
RECALL:
The denominator of a rational expression is not allowed to be equal to zero since division of zero is undefined.
Factor the denominator using the formula $a^2-b^2=(a-b)(a+b)$ to obtain:
$\dfrac{x}{x^2-9} = \dfrac{x}{x^2-3^2}=\dfrac{x}{(x-3)(x+3)}$
Find the values of $x$ that will make the denominator equal to zero by using the zero-factor theorem.
Equate each factor of the denominator to zero, and then solve each equation to obtain:
$\begin{array}{ccc}
\\&x-3 = 0 &\text{ or } &x + 3 = 0
\\&x = 3 &\text{ or } &x=-3
\\\end{array}$
Thus, in the given expression, $x$ cannot be equal to $-3$ or $3$ since they make the denominator equal to 0.
Therefore, the answer is $(a)$.
