Question

Solve the following quadratic equation by factorisation method:
`x/(x + 1) + (x + 1)/x = (34)/(15') x ≠ 0, x ≠ -1`

Answer 1

We have
`x/(x + 1) + (x + 1)/x = (34)/(15)`
⇒ `(x^2 + (x + 1)^2)/(x(x +1)) = (34)/(15)`
⇒ `(x^2 + x^2 + 1 + 2x)/(x^2 + x) = (34)/(15)`
⇒ `(2x^2 + 2x + 1)/(x2 + x) = (34)/(15)`
⇒ 34x² + 34x = 30x² + 30x + 15
⇒ 4x² + 4x - 15 = 0
⇒ 4x² + 10x - 6x - 15 = 0
⇒ 2x(2x + 5) -3(2x + 5) = 0
⇒ (2x + 5) (2x - 3) = 0
⇒ 2x + 5 = 0 or 2x - 3 = 0
⇒ 2x = -5 and 2x = 3
⇒ x = `-(5)/(2), x = (3)/(2)`.