Question

How do you solve `\frac { 1} { x+ 1} - 2= \frac { 2} { x - 2}`?

Answer 1

Make the equation equal to zero by subtracting the `2/(x-2)` on both sides, which makes the equation equal to 0.

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

Then get rid of the denominators since fractions are hard to deal with in these types of problems.

So multiply the whole equation by `(x+1) and (x-2)`

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

Then simplify

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

Then Expand

`x-2-2x^2 +2x +4 - 2x -2 =0`

Simplify

`-2x^2 +x =0`

Factor out a `-x`

`-x(2x-1) = 0`

Solve

`x= 0` and `x= 1/2`