Answer
$\frac{x^2+2x+4}{x+2}$.
Work Step by Step
The given expression is
$=\frac{x^3-8}{x^2-4}$
Factor $x^3-8$.
$=x^3-2^3$
Use the algebraic identity $a^3-b^3=(a-b)(a^2+ab+b^2)$.
$=(x-2)(x^2+2x+4)$.
Factor $x^2-4$.
$=x^2-2^2$
Use the algebraic identity $a^2-b^2=(a+b)(a-b)$.
$=(x+2)(x-2)$.
Substitute all factors into the given expression.
$=\frac{(x-2)(x^2+2x+4)}{(x+2)(x-2)}$
Cancel common terms.
$=\frac{x^2+2x+4}{x+2}$.
