Answer
$x^2-2x+4$
Work Step by Step
Factoring the expressions and then cancelling the common factors between the numerator and the denominator, the given expression, $
\dfrac{x^3+8}{2+x}
$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{(x+2)(x^2-2x+4)}{x+2}
\\\\=
\dfrac{(\cancel{x+2})(x^2-2x+4)}{\cancel{x+2}}
\\\\=
x^2-2x+4
.\end{array}
