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