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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
Hello, Worthey1987!
Could there be a typo in the problem? . . . It's too easy!
Factor -1 out of the numerator: .$\displaystyle \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.Quote:
Simplify: .$\displaystyle \frac{\dfrac{x-y}{x+y} - \dfrac{x+y}{x-y}}{\dfrac{x+y}{x-y} - \dfrac{x-y}{x+y}} $
Just a little colour-coding: $\displaystyle \frac{\ \displaystyle {\color{red}\frac{x-y}{x+y}} - {\color{blue}\frac{x-y}{x+y}} \ }{\ \displaystyle {\color{blue}\frac{x+y}{x-y}} - {\color{red}\frac{x-y}{x+y}} \ }$
Factor out a -1 from the numerator: $\displaystyle = \frac{\ - \left( \displaystyle {\color{blue}\frac{x-y}{x+y}} - {\color{red}\frac{x-y}{x+y}}\right) \ }{\ \displaystyle {\color{blue}\frac{x+y}{x-y}} - {\color{red}\frac{x-y}{x+y}} \ }$
Notice that the thing in parentheses is the same as the same as the bottom. What can you do to them?
