Question

Simplify:

\[\frac{m^2 - n^2}{\left( m + n \right)^2} \times \frac{m^2 + mn + n^2}{m^3 - n^3}\]

Answer 1

We know that,

a³ + b³ = (a + b)(a² − ab + b²)

a³ − b³ = (a − b)(a² + ab + b²)

a² − b²= (a + b) (a − b)

\[\frac{m^2 - n^2}{\left( m + n \right)^2} \times \frac{m^2 + mn + n^2}{m^3 - n^3}\]

\[ = \frac{\left( m + n \right)\left( m - n \right)}{\left( m + n \right)\left( m + n \right)} \times \frac{\left( m^2 + mn + n^2 \right)}{\left( m - n \right)\left( m^2 + mn + n^2 \right)}\]

\[= \frac{1}{m + n}\]