Question

Solve the following equations for the unknown: `(3)/(x + 1) - (x - 6)/(x^2 - 1) = (12)/(x - 1)`

Answer 1

`(3)/(x + 1) - (x - 6)/(x^2 - 1) = (12)/(x - 1)`

`(3)/(x + 1) - (x - 6)/((x - 1)(x + 1)) = (12)/(x - 1)`

LCM of all the denominators in the equation is (x - 1)(x + 1).
Multiply throughout by the LCM.
3(x - 1) - (x - 6) = 12(x + 1)
⇒ 3x - 3 - x + 6 = 12x + 12
⇒ 3x - 12x - x = 12 - 6 + 3
⇒ -10x = 9

⇒ x = `-(9)/(10)`.