Question

Solve equation using factorisation method:

`4/(x + 2) - 1/(x + 3) = 4/(2x + 1)`

Answer 1

`4/(x + 2) - 1/(x + 3) = 4/(2x + 1)`

⇒ `(4(x + 3) - 1(x + 2))/((x + 2)(x + 3)) = 4/(2x + 1)`

⇒ `(4x + 12 - x - 2)/(x^2 + 2x + 3x + 6) = 4/(2x + 1)`

⇒ `(3x + 10)/(x^2 + 5x + 6) = 4/(2x + 1)`

⇒ (3x + 10)(2x + 1) = 4(x² + 5x + 6)

⇒ 6x² + 3x + 20x + 10 = 4x² + 20x + 24

⇒ 2x² + 3x – 14 = 0

⇒ 2x² + 7x – 4x – 14 = 0

⇒ 2x² + 7x – 4x – 14 = 0

⇒ x(2x + 7) – 2(2x + 7) = 0

⇒ (2x + 7)(x – 2) = 0

If 2x + 7 = 0 or x – 2 = 0

Then x = `(-7)/2` or x = 2