Question

Solve the following quadratic equations by factorization:

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

Answer 1

We have been given

`(x+1)/(x-1)-(x-1)/(x+1)=5/6`

6(x² + 1 + 2x - x² - 1 + 2x) = 5(x² - 1)

5x² - 24x - 5 = 0

5x² - 25x + x - 5 = 0

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

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

Therefore,

5x + 1 = 0

5x = -1

x = -1/5

Or,

x - 5 = 0

x = 5

Hence, x = -1/5 or x = 5