#### Answer

$\sqrt[3]{x^2+xy+y^2}$

#### Work Step by Step

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