Question

Solve the following quadratic equations by factorization:

`1/(x - 1) - 1/(x + 5) = 6/7, x ≠ 1, -5`

Answer 1

We have been given

`1/(x-1)-1/(x+5)=6/7`

`6/(x^2+4x-5)=6/7`

x² + 4x - 12 = 0

x² + 6x - 2x - 12 = 0

x(x + 6) - 2(x + 6) = 0

(x + 6)(x - 2) = 0

Therefore,

x - 2 = 0

x = 2

or,

x + 6 = 0

x = -6

Hence, x = 2 or x = -6.