## College Algebra (10th Edition)

$(b)$ and $(d)$
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: $\dfrac{x^3}{x^2-1} = \dfrac{x^3}{x^2-1^2}=\dfrac{x^3}{(x-1)(x+1)}$ 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 then solve each equation to obtain: $\begin{array}{ccc} \\&x-1 = 0 &\text{ or } &x + 1 = 0 \\&x = 1 &\text{ or } &x=-1 \\\end{array}$ Thus, in the given expression, $x$ cannot be equal to $-1$ or $1$ since they make the denominator equal to 0. Therefore, the answer is: $(b)$ and $(d)$.