simplify:

Question

(x^-2 - y^-2) / (x^-1 - y^-1)

i know you have to get rid of the negative powers, but i cant figure out how, any help?

Answer 1

The numerator can be written
(x^-1 + y^-1)(x^-1 -y^-1)
One of the factors cancels the denominator, leaving you with
(x^-1 + y^-1)
Using a common denominator xy, that can be rewritten
(y + x)/xy

Answer 2

multiply top and bottom by (x^2y^2/(x^2y^2))

so

(x^2y^2/(x^2y^2))[(x^-2 - y^-2)/(x^-1 - y^-1)]
= (y^2 - x^2)/(xy^2 - x^2y)
= (y+x)(y-x)/[xy(y-x)]
= (y+x)/(xy)

I usually check a question like that by letting x and y be some numbers, and subbing that back in the original line and the final line.
Here I tried x=3 and y=4, and it worked.

Answer 3

Wow, drwls saw an easier way.
Nice one!

Answer 4

thank you!