What is (x^{-2}-y^{-2})/(x^{-1)y^{-1}} ?

The solution to (x^{-2}-y^{-2})/(x^{-1)y^{-1}} is (y^2-x^2)/(xy)

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simplify (x^{-2}-y^{-2})/(x^{-1)y^{-1}}

simplify

\frac{x ^{- 2} - y ^{- 2}}{x ^{- 1} y ^{- 1}}

\frac{y ^{2} - x ^{2}}{x y}

Solution steps

\frac{x ^{- 2} - y ^{- 2}}{x ^{- 1} y ^{- 1}}

Multiply

x^{- 1} y^{- 1} : \frac{1}{x y}

= \frac{x ^{- 2} - y ^{- 2}}{\frac{1}{x y}}

Simplify

x^{- 2} - y^{- 2} : \frac{1}{x ^{2}} - \frac{1}{y ^{2}}

= \frac{\frac{1}{x ^{2}} - \frac{1}{y ^{2}}}{\frac{1}{x y}}

Join

\frac{1}{x ^{2}} - \frac{1}{y ^{2}} : \frac{y ^{2} - x ^{2}}{x ^{2} y ^{2}}

= \frac{\frac{y ^{2} - x ^{2}}{x ^{2} y ^{2}}}{\frac{1}{x y}}

Divide fractions:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

= \frac{( y ^{2} - x ^{2} ) x y}{x ^{2} y ^{2} \cdot 1}

Refine

= \frac{( y ^{2} - x ^{2} ) x y}{x ^{2} y ^{2}}

Cancel the common factor:

x

= \frac{y ( y ^{2} - x ^{2} )}{x y ^{2}}

Cancel the common factor:

y

= \frac{y ^{2} - x ^{2}}{x y}

\frac{9}{7 + 2}

6 x^{2} - 15 x

- 8 (x) = 2 x^{2} + 2 x - 20

\frac{8}{15} = \frac{m}{11}

\frac{a ^{2}}{a}

What is (x^{-2}-y^{-2})/(x^{-1)y^{-1}} ?
The solution to (x^{-2}-y^{-2})/(x^{-1)y^{-1}} is (y^2-x^2)/(xy)