Question

prove the following- (a+b)^-1 (a^-1+b^-1)=1/ab​

Answer 1

$\star\:\:\bf\large\underline\blue{Given\:To\:Prove:-}$

• ${(a + b)}^{ - 1} \times ( {a}^{ - 1} + {b}^{ - 1} ) = \frac{1}{ab}$

$\star\:\:\bf\large\underline\blue{Solution:-}$

$\star\:\:\bf\underline\blue{LHS:-}$

${(a + b)}^{ - 1} \times ( {a}^{ - 1} + {b}^{ - 1} )$

$= \frac{1}{(a + b)} \times ( \frac{1}{a} + \frac{1}{b} )$

$= \frac{1}{ \cancel{(a + b)}} \times ( \frac{ \cancel{(a + b)}}{ab} )$

$= \frac{1}{ab}$

$= {(ab)}^{ - 1}$

$\star\:\:\bf\underline\blue{RHS:-}$

$= {(ab)}^{ - 1}$

$\bf\underline\blue{Therefore,}$

$\bf\underline\blue{LHS=RHS}$

$\star\:\:\bf\large\underline\blue{Hence\:Proved.}$