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

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

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

simplify

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

x y

Solution steps

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

Simplify

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

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

Apply the fraction rule:

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

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

Cancel

\frac{( 2 x + y ) x y}{y + 2 x} : x y

= x y

48 x^{5}

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