Answer
$(b)\;x=1, (c)\;x=0$ and $(d)\;x=-1$.
Work Step by Step
The given expression is
$=\frac{x^2+5x-10}{x^3-x} $
(a) Substitute $x=3$.
$=\frac{3^2+5(3)-10}{3^3-3} $
Simplify.
$=\frac{9+15-10}{27-3} $
$=\frac{14}{24} $
$=\frac{7}{12} $
(b) Substitute $x=1$.
$=\frac{1^2+5(1)-10}{1^3-1} $
Simplify.
$=\frac{1+5-10}{1-1} $
$=\frac{-4}{0} $
Not defined.
(c) Substitute $x=0$.
$=\frac{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{(-1)^2+5(-1)-10}{(-1)^3-(-1)} $
Simplify.
$=\frac{1-5-10}{-1+1} $
$=\frac{-14}{0} $
Not defined.
Hence, the correct answers are $(b)\;x=1, (c)\;x=0$ and $(d)\;x=-1$.
