Question

How do you solve `\frac { 2} { x + 2} - \frac { 1} { x - 2} = \frac { 2x } { x ^ { 2} - 4}`?

Answer 1

`x=-6`

Explanation:

Given:

`2/(x+2)-1/(x-2) = (2x)/(x^2-4)`

Note that:

`(x-2)(x+2) = x^2-4`

So multiplying the whole equation by `x^2-4` we get:

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

That is:

`x-6 = 2x`

Subtracting `x` from both sides, we find:

`x = -6`

This is a valid solution of the original equation, since it is not a zero of `x^2-4`.