1. simplify fraction

Hey, this one's probably real simple, but I'm stuck.

I'd like to see the work and answer for performing the operations and simplifying this:

x-y - x+y
x+y x-y
x+y - x-y
x-y x+y

I'd appreciate any help. Like I said I'm sure it's easy, I'm just stuck.

-Worthey1987

2. Hello, Worthey1987!

Could there be a typo in the problem? . . . It's too easy!

Simplify: . $\frac{\dfrac{x-y}{x+y} - \dfrac{x+y}{x-y}}{\dfrac{x+y}{x-y} - \dfrac{x-y}{x+y}}$
Factor -1 out of the numerator: . $\frac{\text{-}1\bigg[\dfrac{x+y}{x-y} - \dfrac{x-y}{x+y}\bigg]}{\;\;\;\bigg[\dfrac{x+y}{x-y} - \dfrac{x-y}{x+y}\bigg]}$ . . . and reduce.

3. Just a little colour-coding: $\frac{\ \displaystyle {\color{red}\frac{x-y}{x+y}} - {\color{blue}\frac{x-y}{x+y}} \ }{\ \displaystyle {\color{blue}\frac{x+y}{x-y}} - {\color{red}\frac{x-y}{x+y}} \ }$

Factor out a -1 from the numerator: $= \frac{\ - \left( \displaystyle {\color{blue}\frac{x-y}{x+y}} - {\color{red}\frac{x-y}{x+y}}\right) \ }{\ \displaystyle {\color{blue}\frac{x+y}{x-y}} - {\color{red}\frac{x-y}{x+y}} \ }$

Notice that the thing in parentheses is the same as the same as the bottom. What can you do to them?