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

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

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

simplify

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

\frac{y - x}{y}

Solution steps

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

Apply exponent rule:

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

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

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

Apply the fraction rule:

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

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

Simplify

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

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

Join

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

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

Apply the fraction rule:

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

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

x y x^{- 1} = y

= \frac{y - x}{y}

\frac{x ^{2} - 1}{5 x ^{2} + 4 x - 9}

\frac{1}{2 0}

lo g_{2} (64000)

\frac{6 !}{3 ! 2 !}

12 + 27 + 48

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