Question

Solve for x , (x+1)/(x-1) + (x-1)/(x+1) = 5/6 , x ≠1 , x ≠-1

Answer 1

Answer:

Hope this will help you..........

Answer 2

Correct question

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

Step-by-step explanation:

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

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

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

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

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

$⟹ {5x}^{2} - 5 = 24x$

$⟹ {5x}^{2} - 24x - 5 = 0$

$⟹5 {x}^{2} - 25x + x - 5 = 0$

$⟹5x(x - 5) + 1(x - 5) = 0$

$⟹(x - 5)(5x + 1) = 0$

$⟹x - 5 = 0 \: \: or \: \: 5x + 1 = 0$

$∴ \: \: \: \: \: \: \: x = 5 \: \: or \: \: x = \frac{ - 1}{5}$

Thus, roots of equation are 5 and - 1/5