Question

Prove this question.
Thankyou ​

Answer 1

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

$\implies ( \frac{1}{a + b} ) {( \frac{1}{a} + \frac{1}{b} )}$

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

$\implies \frac{1}{ab}$

$\therefore {(ab)}^{ - 1}$

$\purple{ \sf Hence \: \: Proved.}$