Question

Simlify:
$\frac{m^2-n^2}{{\left(m+n\right)}^2}\times \frac{m^2+mn+n^2}{m^3-n^3}$

Answer 1

$\frac{m^2-n^2}{(m+n{)}^2}\times \frac{(m^2+mn+n^2)}{(m^3-n^3)}$

$\left[\begin{array}{c}\because a^2-b^2=(a-b)(a+b)\\ a^3-b^3=(a-b)(a^2+b^2+ab)\end{array}\right]$

$\Rightarrow \frac{(m-n)(m+n)\times (m^2+mn+n^2)}{(m+n{)}^2\times (m-n\left)\right(m^2+n^2+mn)}$

$=\frac{1}{m+n}$.