Question

solve the following
​

Answer 1

Answer:

The answer is

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

Step-by-step explanation:

Given

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

We know that

${x}^{2} - {y}^{2} = (x + y)(x - y)$

${x}^{3} - {y}^{3} = (x - y)( {x}^{2} + xy + {y}^{2} )$

Hence,

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

After common factor cancellations, we have the answer as

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