Question

Solve for x :

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

Answer 1

`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 = 1`