Question

find the roots of the following equation by factorisation. x+1/x-1- x-1/x+1=5/6: X doesn't equal to 1,-1​

Answer 1

x = -
`(1)/(5)`, x = 5

Explanation:

Given

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

Multiply through by 6(x - 1)(x + 1) [ the LCM of the denominators ]

6(x + 1)² - 6(x - 1)² = 5(x - 1)(x + 1) ← expand factors and simplify

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

6x² + 12x + 6 - 6x² + 12x - 6 = 5x² - 5

24x = 5x² - 5 ( subtract 24x from both sides )

0 = 5x² - 24x - 5 ← in standard form

0 = (x - 5)(5x + 1) ← in factored form

Equate each factor to zero and solve for x

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

x - 5 = 0 ⇒ x = 5

Answer 2

x= -1/5

hope this helps you