Answer
$\sqrt[3] {x+3}$.
Work Step by Step
The given expression is
$\frac{\sqrt[3] {x^2+5x+6}}{\sqrt[3] {x+2}}$
Use the quotient rule $\frac{\sqrt[n] a}{\sqrt[n] b} = \sqrt[n] {\frac{a}{b}}$.
$=\sqrt[3] {\frac{x^2+5x+6}{x+2}}$
Factor the numerator.
$=\sqrt[3] {\frac{x^2+3x+2x+6}{x+2}}$
$=\sqrt[3] {\frac{x(x+3)+2(x+3)}{x+2}}$
$=\sqrt[3] {\frac{(x+3)(x+2)}{x+2}}$
Cancel out common terms.
$=\sqrt[3] {x+3}$.
