Asked by Joanne

X^-2 - Y^-2
__________

X^-1 + Y-1
Answered by Reiny
= (1/x^2 - 1/y^2) / (1/x + 1/y)
= (1/x + 1/y)(1/x - 1/y)/(1/x + 1/y)
= 1/x - 1/y
or
(y-x)/(xy)

OR

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