Question

Solve the following equations for the unknown: `(x + 13)/(x^2 - 1) + (5)/(x + 1) = (7)/(x + 1)`

Answer 1

`(x + 13)/(x^2 - 1) + (5)/(x + 1) = (7)/(x + 1)`

⇒ `(x + 13)/((x - 1)(x + 1)) + (5)/(x + 1) = (7)/(x + 1)`

LCM of all the denominators in the equation is (x -1)(x + 1).
Multiply throughout by the LCM.
x + 13 + 5(x - 1) = 7(x - 1)
⇒ x + 13 + 5x - 5 = 7x - 7
⇒ 13 - 5 + 7 = 7x - 5x - x
⇒ x = 15.