Question

Q. 7
Find the roots of the following equation by Factorisation
x+1/x-1 - x-1 / x+1 =5/6
x not equal to 1 ,-1​

Answer 1

Answer:

$x = 5 \: and \: x = \frac{1}{5}$

Step-by-step explanation:

$\frac{x + 1}{x - 1} - \frac{x - 1}{x + 1} = \frac{5}{6}$

$\frac{ {(x + 1)}^{2} - {(x - 1)}^{2} }{(x - 1)(x + 1)} = \frac{5}{6}$

$\frac{( {x}^{2} + 1 + 2x) - ( {x}^{2} + 1 - 2x )}{x(x +1) - 1(x + 1)} = \frac{5}{6}$

$\frac{ {x}^{2} + 1 + 2x - {x}^{2} - 1 + 2x }{ {x}^{2} + x - x - 1 } = \frac{5}{6}$

$\frac{ {x}^{2} - {x}^{2} + 1 - 1 + 2x + 2x }{ {x}^{2} - 1 } = \frac{5}{6}$

$\frac{4x}{ {x}^{2} - 1 } = \frac{5}{6}$

$5( {x}^{2} - 1) = 6(4x)$

$5 {x}^{2} - 5 = 24x$

$5 {x}^{2} - 24x - 5 = 0$

$5 {x}^{2} - 25x + x - 5 = 0$

$(5 {x}^{2} - 25x) + (x - 5) = 0$

$5x(x - 5) + 1(x - 5) = 0$

$(x - 5)(5x - 1) = 0$

$(x - 5 = 0)(5x - 1 = 0)$

$x = 5 \: and \: x = \frac{1}{5}$