algebra question?

Question

-1 -1
X - Y
_____
-2 -2
X - Y

Answer 1

Multiply by x² y² numerator and denominator
So you have :
(xy²-yx²)/(y²-x²)
Factorizing numerator and denominator :
xy (y-x)/ ((y-x) (y+x))
So it is :
xy/(y+x)

Answer 2

Do I understand you to mean:
(x^(-1) - y^(-1))/(x^(-2) - y^(-2))
And you're asking us how to simplify this?

First, multiply the fraction by x²y²/(x²y²):

(xy² - yx²)/(y² - x²)

Next, factor:

xy(y-x)/((y-x)(y+x))

Cancel out the common factor:

xy/(y+x)

And the fraction is thus simplified.