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# simplify complex fraction help?

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

can someone help me step by step

thank you

### 2 Answers

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- Anonymous9 years ago
If your question is to simplify (x^-2 - y^-2 )/ (1/x - 1/y), then multiply numerator & denominator by xy:

xy(x^-2 - y^-2 )/(y-x) = xy(x+y)(x-y)/(-(x-y)) = -xy(x+y)

- DavidLv 79 years ago
(X^-2 - Y^-2) / [(1/X) - (1/Y)]

(X^-2 - Y^-2) / [(Y - X) / XY]

XY(X^-2 - Y^-2) / (Y - X)

(X^-1Y - XY^-1) / (Y - X)

[(Y/X) - (X/Y)] / (Y - X)

[(Y^2 - X^2) / XY] / (Y - X)

(Y + X)(Y - X) / [XY(Y - X)]

(Y + X) / XY

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