Question

How do you simplify `x/(x+2) - x/(x-2)`?

Answer 1

`-(4x)/((x-2)(x+2))`

Explanation:

You need to find the common denominator of the two fractions. Notice that you can multiply the first fraction by `1 = (x-2)/(x-2)` and the second fraction by `1 = (x+2)/(x+2)` to get

`x/(x+2) * (x-2)/(x-2) - x/(x-2) * (x+2)/(x+2)`

`( x * (x-2))/((x-2)(x+2)) - ( x * (x+2))/((x-2)(x+2))`

Expand the parantheses in the numerator to cancel out like terms

`( color(red)(cancel(color(black)(x^2))) - 2x - color(red)(cancel(color(black)(x^2))) - 2x)/((x-2)(x+2))`

The final form of the expression will thus be

`-(4x)/((x-2)(x+2))`