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