Question

Solve the following quadratic equation:

`1/(x - 1) - 1/(x + 5) = 6/7, x ≠ 1, -5`

Answer 1

`1/(x - 1) - 1/(x + 5) = 6/7, x ≠ 1, -5`  

⇒ `(x + 5 - x + 1)/((x - 1)(x + 5)) = 6/7` 

⇒ `6/(x^2 + 4x - 5) = 6/7` 

⇒ x² + 4x – 5 = 7 

⇒ x² + 4x – 12 = 0 

⇒ x² + 6x – 2x – 12 = 0 

⇒ x(x + 6) – 2(x + 6) = 0 

⇒ (x + 6)(x – 2) = 0 

⇒ x + 6 = 0 or x – 2 = 0

⇒ x = –6 or x = 2 

Hence, –6 and 2 are the roots of the given equation.