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

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

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

simplify

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

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

Solution steps

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

Apply exponent rule:

a^{- 1} = \frac{1}{a}

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

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

Simplify

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

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

Join

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

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

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

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

\frac{\frac{1}{8}}{3}

2 x - 4 = 7

- \frac{π}{4} \cdot \frac{1}{2}

\frac{1}{5} a^{3} - \frac{3}{5} a^{2} + \frac{4}{5} a

\frac{4}{\frac{3}{4} - \frac{3}{2}}

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