Question

prove this equation given above ,give complete step by step explanation​

Answer 1

Step-by-step explanation:

$\huge\sf\green{Answer}$

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

$\longrightarrow$

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

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

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

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

$lhs = rhs$

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

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

${b}^{2} - {a}^{2} - 2 {b}^{2} = 0$

$- {b}^{2} - {a}^{2} = 0$

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

$\longrightarrow$

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

$b = a$

$hence \: proved \:this \: is \: urs \: answer$