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Simplify the ...

Question

Simplify the following expression:
$(\frac{1}{(m + n)^{2}} (\frac{1}{m^{2}} + \frac{1}{n^{2}}) + \frac{2}{(m + n)^{3}} (\frac{1}{m} + \frac{1}{n})) m^{2} n^{2}$

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Solution

$\frac{(m n)^{2}}{m n (m + n)^{2}} (\frac{m^{2} + n^{2}}{m n} + \frac{2 (m + n)}{(m + n)}) = \frac{m n}{(m + n)^{2}} (\frac{(m + n)^{2}}{m n}) = 1$

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