Question

Solve the following equation by factorisation method:

`(x-1)/(x+1) + (x+1)/(x-1) = 29/10, x\cancel= 1, -1`

Answer 1

Given:

`(x-1)/(x+1) + (x+1)/(x-1) = 29/10, x\cancel= 1, -1`

Take LCM (x + 1) and combine

`((x-1)^2 + (x+1)^2)/((x+1)(x-1))= 29/10`

Simplify the numerator

(x − 1)² + (x + 1)² = (x² − 2x + 1) + (x² + 2x + 1) = 2x² + 2

`(2(x^2+1))/(x^2-1) = 29/10`

20(x² + 1) = 29(x² − 1)

20x² + 20 = 29x² − 29

9x² − 49 = 0

(3x − 7) (3x + 7) = 0

3x − 7 = 0

⇒ x = `7/3`

3x + 7 = 0

⇒ x = −`7/3`

x = `7/3` or x = −`7/3`