Question

solve (a^_1+b^_1)^_1=ab/a+b​

Answer 1

$\large{ \bold{\pink{LHS }}}= {( {a}^{ - 1} + {b}^{ - 1}) }^{ - 1} \\ = { (\dfrac{1}{a} + \dfrac{1}{b} )}^{ - 1} \\ = { ( \: \: \dfrac{b + a}{ab} \: \: )}^{ - 1} \\ = {( \: \dfrac{ab}{b + a}) \: } ^{ + 1} \\ = \dfrac{ab}{a + b} = \pink{ \bold{ \large{RHS}}}$

$\red{ \bold {\large{ \underline{ \underline{Formula \: used}}}}} \pink{ \bold{\longrightarrow}} \\ \bold{ \blue{1. \: \: \: \: \: \: \: \boxed{ \boxed{ \bold{{a}^{ - n} = \dfrac{1}{ {a}^{n}}}}}}}$