Question

Solve the following equation by factorization:

`(x + 1)/(x - 1) = (3x - 7)/(2x - 5)`

Answer 1

Given,

⇒ `(x + 1)/(x - 1) = (3x - 7)/(2x - 5)`

⇒ (x + 1)(2x – 5) = (3x – 7)(x – 1)

⇒ (2x² – 5x + 2x – 5) = (3x² – 3x – 7x + 7)

⇒ (2x² – 3x – 5) = (3x² – 10x + 7)

⇒ (3x² – 10x + 7) – (2x² – 3x – 5) = 0

⇒ 3x² – 10x + 7 – 2x² + 3x + 5 = 0

⇒ x² – 7x + 12 = 0

⇒ x² – 3x – 4x + 12 = 0

⇒ x(x – 3) – 4(x – 3) = 0

⇒ (x – 4)(x – 3) = 0

⇒ (x – 4) = 0 or (x – 3) = 0   ...[Using zero-product rule]

⇒ x = 4 or x = 3

Hence, x = {3, 4}.