Question

Solve the following equation by factorization:

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

Answer 1

Given,

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

⇒ (3x + 1)(7x + 5) = (5x + 1)(7x + 1)

⇒ (21x² + 15x + 7x + 5) = (35x² + 5x + 7x + 1)

⇒ (21x² + 22x + 5) = (35x² + 12x + 1)

⇒ (35x² + 12x + 1) – (21x² + 22x + 5) = 0

⇒ 35x² + 12x + 1 – 21x² – 22x – 5 = 0

⇒ 14x² – 10x – 4 = 0

⇒ 2(7x² – 5x – 2) = 0

⇒ 7x² – 5x – 2 = 0

⇒ 7x² – 7x + 2x – 2 = 0

⇒ 7x(x – 1) + 2(x – 1) = 0

⇒ (7x + 2)(x – 1) = 0

⇒ (7x + 2) = 0 or (x – 1) = 0   ...[Using zero-product rule]

⇒ 7x = –2 or x = 1

⇒ x = `(-2)/7` or x = 1

Hence, `x = {1, (-2)/7}`.