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

Question

Solve: \(\frac{x + 1}{x - 1}-\frac{x -1}{x+1}=\frac56, x≠1,-1.\)

Answer 1

⇒ 5x² - 24x -5 = 0 ⇒ 5x² - 25x + \(x\) - 5 = 0

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

⇒ (x - 5) = 0 or (5x + ) = 0

⇒ x = 5, \(\frac{-1}{5}.\)