Question

please give me right solution ... please . faster plzz ...​

Answer 1

Answer:

Here is your solution.. Thanks

Answer 2

Solution →

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

LHS →

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

We can write

${x}^{ - 1}$

as -

${x}^{ - 1} = \frac{1}{x}$

So,

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

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

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

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

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

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

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

RHS

Hence Proved !!

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