Question
Simplify $\frac{x^3}{x-y}+\frac{y^3}{y-x}$
✓
Answer
$\begin{aligned} & =\frac{x^3}{x-y}-\frac{y^3}{x-y} \\ & =\frac{x^3-y^3}{x-y} \ldots\left(\text { using } a ^3- b ^3=( a - b )\left( a ^2+ ab + b ^2\right)\right) \\ & =\frac{(x-y)\left(x^2+x y+y^2\right)}{x-y} \\ & = x ^2+ xy + y ^2\end{aligned}$
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