Question

$(m+n)^{-1} (m^{-1}+n^{-1} )$

Answer 1

Step-by-step explanation:

$\sf \mapsto {(m + n)}^{ - 1} ( {m}^{ - 1} + {n}^{ - 1} ) \\ \sf \mapsto (\frac{1}{m + n} )( \frac{1}{m} + \frac{1}{n} ) \\ \sf \mapsto( \frac{1}{m + n} )( \frac{m + n}{mn} ) \\ \sf \mapsto \frac{m + n}{m {}^{2} + {n}^{2} }$

Answer 2

final answer:-

$(m+n)^{-2}$

given:-

$(m+n)^{-1}(m^{-1}+n^{-1})$

concept used:-

$(a+b)^{x}(a+b)^{y}=(a+b)^{x+y}$

solution:-

$(m^{-1}+n^{-1})$ ⇒$(m+n)^{-1}$

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

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