Question
Simplify : $\frac{m^2-n^2}{(m+n)^2} \times \frac{m^2+m n+n^2}{m^3-n^3}$
✓
Answer
$\begin{aligned} & \text {} \frac{m^2-n^2}{(m+n)^2} \times \frac{m^2+m n+n^2}{m^3-n^3} \\ & \frac{\mathrm{m}^2-\mathrm{n}^2}{(\mathrm{~m}+\mathrm{n})^2} \times \frac{\mathrm{m}^2+\mathrm{mn}+\mathrm{n}^2}{\mathrm{~m}^3-\mathrm{n}^3} \\ & =\frac{(\mathrm{m}+\mathrm{n})(\mathrm{m}-\mathrm{n})}{(\mathrm{m}+\mathrm{n})(\mathrm{m}+\mathrm{n})} \times \frac{\mathrm{m}^2+\mathrm{mn}+\mathrm{n}^2}{(\mathrm{~m}-\mathrm{n})\left(\mathrm{m}^2+\mathrm{mn}+\mathrm{n}^2\right)} \\ & =\frac{\mathbf{1}}{\mathbf{m}+\mathbf{n}}\end{aligned}$
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