#### Answer

$\sqrt[3]{r^2-rs+s^2}$

#### Work Step by Step

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.