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Solve for X : `1by(X + 1) + 3by(5x + 1) = 5by(X + 4), X Not Equal -1, -1by5, -4` - CBSE Class 10 - Mathematics

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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)

⇒8x2 + 32x + 4x + 16 = 5(5x2 +x + 5x +1)

⇒8x2 +36x +16 =25x2 +30x +5

⇒17x2 −6x −11 =0

⇒17x2 − 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.
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