Question

Find the roots of the following equation by Factorisation.
x+1/x-1 - x-1/x+1 = ⅚ ; x≠1,-1
​

Answer 1

Step-by-step explanation:

$\frac{x + 1}{x - 1} - \frac{x - 1}{x + 1}$

$= \frac{(x + 1)(x + 1)}{(x - 1)( x+ 1)} + \frac{(x - 1)(x - 1)}{(x + 1)(x - 1)}$

$= \frac{ {x}^{2} + 2x + 1 }{ {x}^{2} - 1 } + \frac{ {x}^{2} - 2x + 1}{ {x}^{2} - 1 }$

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

$= \frac{ {x }^{2} + 2x + 1 - {x}^{2} + 2x - 1 }{ {x}^{2} - 1}$

$= \frac{4x}{ {x}^{2} - 1}$