Question

Solve the following equation by factorisation method:

`1/x + ((x-1))/2 = x, x\cancel=0`

Answer 1

Given:

`1/x + ((x-1))/2 = x, x\cancel=0`

Take LCM of denominators = 2x

Multiply the whole equation by 2x:

2 + x(x − 1) = 2x²

2 + x² − x = 2x²

0 = 2x² − x² + x − 2

x² + x − 2 = 0

Two numbers whose product = −2 and sum = 1:

2 and −1

(x + 2) (x − 1) = 0

x + 2 = 0

⇒ x = −2

x − 1 = 0

⇒ x = 1

x = −2 or x = 1