#### Question

Solve for x :

`1/(x + 1) + 3/(5x + 1) = 5/(x + 4), x != -1, -1/5, -4`

#### Solution

`1/(x + 1) + 3/(5x + 1) = 5/(x + 4), x != -1, -1/5, -4`

`=> (5x + 1+3x + 3)/((x `+ 1)(5x + 1)) = 5/(x+4)`

⇒(8x + 4)(x + 4) =5(x + 1)(5x + 1)

⇒8x^{2} + 32x + 4x + 16 = 5(5x^{2} +x + 5x +1)

⇒8x^{2} +36x +16 =25x^{2} +30x +5

⇒17x^{2} −6x −11 =0

⇒17x^{2} − 17x + 11x − 11 = 0

⇒17x(x − 1) + 11(x − 1) = 0

⇒(17x + 11)(x − 1) = 0

⇒17x + 11 = 0 or x − 1 = 0

`=> x = -11/17 or x = 11`

Is there an error in this question or solution?

Solution Solve for X : `1by(X + 1) + 3by(5x + 1) = 5by(X + 4), X Not Equal -1, -1by5, -4` Concept: Solutions of Quadratic Equations by Factorization.