What is (a^{-2}-b^{-2})^{-1} ?

The solution to (a^{-2}-b^{-2})^{-1} is (a^2b^2)/(b^2-a^2)

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simplify (a^{-2}-b^{-2})^{-1}

simplify

(a^{- 2} - b^{- 2})^{- 1}

\frac{a ^{2} b ^{2}}{b ^{2} - a ^{2}}

Solution steps

(a^{- 2} - b^{- 2})^{- 1}

Apply exponent rule:

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

(a^{- 2} - b^{- 2})^{- 1} = \frac{1}{a ^{- 2} - b ^{- 2}}

= \frac{1}{a ^{- 2} - b ^{- 2}}

Simplify

a^{- 2} - b^{- 2} : \frac{1}{a ^{2}} - \frac{1}{b ^{2}}

= \frac{1}{\frac{1}{a ^{2}} - \frac{1}{b ^{2}}}

Join

\frac{1}{a ^{2}} - \frac{1}{b ^{2}} : \frac{b ^{2} - a ^{2}}{a ^{2} b ^{2}}

= \frac{1}{\frac{b ^{2} - a ^{2}}{a ^{2} b ^{2}}}

Apply the fraction rule:

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

= \frac{a ^{2} b ^{2}}{b ^{2} - a ^{2}}

(1 6^{3}) \frac{1}{4}

(x^{2} - 2 x - 2) (3 x^{2} - 4 x + 4)

\frac{x ^{12}}{x ^{3}}

\frac{- a ^{2} b}{- ab}

\frac{\frac{2 x + 5}{4}}{\frac{2 x + 5}{6}}

What is (a^{-2}-b^{-2})^{-1} ?
The solution to (a^{-2}-b^{-2})^{-1} is (a^2b^2)/(b^2-a^2)