## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$\sqrt[3]{r^2-rs+s^2}$
Using the properties of radicals, the given expression, $\dfrac{\sqrt[3]{r^3+s^3}}{\sqrt[3]{r+s}} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt[3]{\dfrac{r^3+s^3}{r+s}} \\\\= \sqrt[3]{\dfrac{(r+s)(r^2-rs+s^2)}{r+s}} \\\\= \sqrt[3]{\dfrac{(\cancel{r+s})(r^2-rs+s^2)}{\cancel{r+s}}} \\\\= \sqrt[3]{r^2-rs+s^2} .\end{array} * Note that it is assumed that all variables represent positive numbers.