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

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

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

simplify

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

\frac{x y}{y - x}

Solution steps

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

Apply exponent rule:

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

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

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

Simplify

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

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

Join

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

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

Apply the fraction rule:

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

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

\frac{x ^{2} - 7 x - 8}{x ^{2} - 64}

2^{6 l o g_{4} (n) + 7}

- 5 \div 1

4.5 \cdot 1 0^{4}

- 14 - (- 7)

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