Answer
$(c)$
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 to obtain:
$\dfrac{-9x^2-x+1}{x^3+x} = \dfrac{-9x^2-x+1}{x(x^2+1)}$
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:
$\begin{array}{ccc}
\\&x = 0 &\text{ or } &x^2+1 = 0
\\&x=0 &\text{ or } &x^2=-1
\\\end{array}$
No real number satisfies the second equation.
Thus, in the given expression, $x$ cannot be equal to $0$ since it will make the denominator equal to 0.
Therefore, the answer is: $(c)$.
