precalc

simplify:
(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?

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  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

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  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.

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  3. Wow, drwls saw an easier way.
    Nice one!

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  4. thank you!

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