Question

How do you solve `(x-2)/(x+5) - 4/(x+1) = 1/(x+1)`?

Answer 1

`x=9` or `x=-3`

Explanation:

First, lets rewrite the equation in the form

`(x-2)/(x+5) - 5/(x+1) = 0`

Then we multiply both sides of the equation by `(x+5)(x+1)` to get rid of the denominators.

This changes the equation to

`(x-2)(x+1)-5(x+5)=0 implies`
`(x^2-x-2)-(5x+25)=0 implies`
`x^2-6x-27=0 implies`
`x^2-9x+3x-27=0 implies`
`x(x-9)+3(x-9)=0 implies`
`(x-9)(x+3)=0`

Thus, either `x=9` or `x=-3`