Question

यदि A = x+1/x-1 तो A-1/A का मान ज्ञात कीजिए

Answer 1

if A= x +1 / x-1 then
A - 1/A =
x+1/x-1 - x-1 / x+1
(x+1)^2 - (x-1)^2 /x^2 -1
x^2 +2x +1 - x^2 +2x -1 /x^2-1
4x / x^2 -1

Answer 2

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$\bold{\underline{Question-}}$

यदि A = x+1/x-1 तो A-1/A का मान ज्ञात कीजिए


$\bold{\underline{Answer-}}$


हल -

A = x+1 / x-1 तब, 1/A = x-1 / x+1

अब, A-1/A

$= > \frac{x + 1}{x - 1} - \frac{x - 1}{x + 1} \\ \\ \\ \\ = > \frac{( {x + 1})^{2} - {(x - 1)}^{2} }{(x - 1)(x + 1) } \\ \\ \\ \\ \\ = > \frac{( {x}^{2} + 2x + 1) - ( {x}^{2} - 2x + 1) }{ {x}^{2} - 1} \\ \\ \\ \\ \\ = > \frac{ {x}^{2} + 2x + 1 - {x}^{2} + 2x - 1 }{ {x}^{2} - 1 } \\ \\ \\ \\ \\ = > \frac{4x}{ {x}^{2} - 1}$