Answer
$x-y$
Work Step by Step
The given expression, $
\dfrac{x^2-y^2}{(x-y)^2}\cdot\dfrac{x^2-xy+y^2}{x^2-2xy+y^2}\div\dfrac{x^3+y^3}{(x-y)^4}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{x^2-y^2}{(x-y)^2}\cdot\dfrac{x^2-xy+y^2}{x^2-2xy+y^2}\cdot\dfrac{(x-y)^4}{x^3+y^3}
\\\\=
\dfrac{(x+y)(x-y)}{(x-y)^2}\cdot\dfrac{x^2-xy+y^2}{(x-y)(x-y)}\cdot\dfrac{(x-y)^4}{(x+y)(x^2-xy+y^2)}
\\\\=
\dfrac{(\cancel{x+y})(x-y)}{(x-y)^2}\cdot\dfrac{\cancel{x^2-xy+y^2}}{(x-y)(x-y)}\cdot\dfrac{(x-y)^4}{(\cancel{x+y})(\cancel{x^2-xy+y^2})}
\\\\=
\dfrac{(x-y)^5}{(x-y)^4}
\\\\=
\dfrac{\cancel{(x-y)^4}(x-y)}{\cancel{(x-y)^4}}
\\\\=
x-y
.\end{array}
