Question

Solve the following equation by factorisation method:

`(x+4)/(x+5) - x/(x+1) = 1/8, x \cancel= -5,-1`

Answer 1

Given:

`(x+4)/(x+5) - x/(x+1) = 1/8, x \cancel= -5,-1`

Take LCM (x + 5) (x + 1)

`((x+4) (x+1) -x(x+5))/((x+5)(x+1)) = 1/8`

(x + 4) (x + 1) = x² + 5x + 4

x(x + 5) = x² + 5x

(x² + 5x + 4) − (x² + 5x) = 4

`4/((x+5)(x+1)) = 1/8`

32 = (x + 5) (x + 1)

x² + 6x + 5 − 32 = 0

x² + 6x − 27 = 0

Find two numbers whose product is −27 and sum is 6:

9 and −3

(x + 9) (x − 3) = 0

x + 9 = 0

⇒ x = −9

x − 3 = 0

⇒ x = 3

x = −9 or x = 3​