Question

Solve the following equation by factorisation method:

`(x+1)/x + x/(x+1) = 4 1/4, x\cancel=0, -1`

Answer 1

Given:

`(x+1)/x + x/(x+1) = 4 1/4, x\cancel=0, -1`

`4 1/4`

`=17/4`

So, 

`(x+1)/x + x/(x+1)`

`=17/4`

Take LCM = x(x+1) and multiply throughout

`(x+1)^2 + x^2`

`= 17/4 x (x+1)`

Multiply both sides by 4:

4(x + 1)² + 4x² = 17x(x + 1)

4(x² + 2x + 1) + 4x² = 17(x² + x)

4x² + 8x + 4 + 4x² = 17x² + 17x

8x² + 8x + 4 = 17x² + 17x

0 = 17x² + 17x − 8x² − 8x − 4

Product = 9 × (−4)

= −36

= 9 

9x² + 12x − 3x − 4 = 0

3x(3x + 4) − 1(3x + 4) = 0

(3x + 4) (3x − 1) = 0

3x + 4 = 0

⇒ x = −`4/3`

3x − 1 = 0

⇒ x = `1/3`

x = −`4/3` or x = `1/3`