Answer
$\sqrt[3] {x+4}$.
Work Step by Step
The given expression is
$\frac{\sqrt[3] {x^2+7x+12}}{\sqrt[3] {x+3}}$
Use the quotient rule $\frac{\sqrt[n] a}{\sqrt[n] b} = \sqrt[n] {\frac{a}{b}}$.
$=\sqrt[3] {\frac{x^2+7x+12}{x+3}}$
Factor the numerator.
$=\sqrt[3] {\frac{x^2+4x+3x+12}{x+3}}$
$=\sqrt[3] {\frac{x(x+4)+3(x+4)}{x+3}}$
$=\sqrt[3] {\frac{(x+4)(x+3)}{x+3}}$
Cancel out common terms.
$=\sqrt[3] {x+4}$.
