Answer
$(c)\;x=0$.
Work Step by Step
The given expression is
$=\frac{-9x^2-x+1}{x^3+x} $
(a) Substitute $x=3$.
$=\frac{-9(3)^2-(3)+1}{3^3+3} $
Simplify.
$=\frac{-81-3+1}{27+3} $
$=\frac{-83}{30} $
(b) Substitute $x=1$.
$=\frac{-9(1)^2-(1)+1}{1^3+1} $
Simplify.
$=\frac{-9-1+1}{1+1} $
$=\frac{-9}{2} $
$=-\frac{9}{2} $
(c) Substitute $x=0$.
$=\frac{-9(0)^2+5(0)-10}{0^3+0} $
Simplify.
$=\frac{0+0-10}{0+0} $
$=\frac{-10}{0} $
Not defined.
(d) Substitute $x=-1$.
$=\frac{-9(-1)^2-(-1)+1}{(-1)^3-1} $
Simplify.
$=\frac{-9+1+1}{-1-1} $
$=\frac{-6}{-2} $
$=3$
Hence, the correct answer is $(c)\;x=0$.
