Question

plss tell quickly solving in notebook​

Answer 1

To prove -

$\frac{ {a}^{ - 1} }{ {a}^{ - 1} + {b}^{ - 1} } + \frac{ {a}^{ - 1} }{ {a}^{ - 1} - {b}^{ - 1} } = \frac{2 {b}^{2} }{ {b}^{2} - {a}^{2} }$

Proof -

L. H. S

$= \frac{ {a}^{ - 1} }{ {a}^{ - 1} + {b}^{ - 1} } + \frac{ {a}^{ - 1} }{ {a}^{ - 1} - {b}^{ - 1} }$

$= \frac{ \frac{1}{a} }{ \frac{1}{a} + \frac{1}{b} } + \frac{ \frac{1}{a} }{ \frac{1}{a} - \frac{1}{b} }$

$= \frac{ \frac{1}{a} }{ \frac{b + a}{ab} } + \frac{ \frac{1}{a} }{ \frac{b - a}{ab} }$

$= \frac{1}{a} \div \frac{b + a}{ab} + \frac{1}{a} \div \frac{b - a}{ab}$

$= \frac{1}{a} \times \frac{ab}{b + a} + \frac{1}{a} \times \frac{ab}{b - a}$

$= \frac{b}{b + a} + \frac{b}{b - a}$

$= \frac{b(b - a) + b(b + a)}{(b + a)(b - a)}$

$= \frac{ {b}^{2} - ab + {b}^{2} + ab }{ {b}^{2} - {a}^{2} }$

$= \frac{2 {b}^{2} }{ {b}^{2} - {a}^{2} }$

R. H. S

Proved