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

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

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

simplify

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

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

Solution steps

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

Simplify

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

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

Simplify

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

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

Apply the fraction rule:

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

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

Cancel the common factor:

x

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

(4 x) (4 x)

(5 x^{2} + 2)^{2}

(x^{2} + x - 1) (3 x^{2} + 6 x + 6)

3 x (x - 5)

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