Question

Solve equation using factorisation method:

`(1 + 1/(x+1))(1-1/(x-1)) = 7/8`

Answer 1

`(1 + 1/(x+1))(1-1/(x-1)) = 7/8`

Step 1: Expand the left-hand side

`(1+ 1/(x-1))(1- 1/(x-1)) = 1-1/(x-1) + 1/(x+1) - 1/((x+1)(x-1))`

`1 - 1/(x-1) + 1/(x+1)- 1/(x^2-1) = 7/8`

Combine fractions with common denominators where necessary. We'll simplify and solve for x.

The solutions to the equation

`(1 + 1/(x+1))(1-1/(x-1)) = 7/8`

x = −5 and x = 5