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

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

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

simplify

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

y + x

Solution steps

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

Simplify

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

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

Apply the fraction rule:

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

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

Simplify

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

= \frac{y + x}{1}

Apply the fraction rule:

\frac{a}{1} = a

= y + x

- \frac{3}{2}

34 x + 78 = x^{2} + 34 x - 43

(\frac{x ^{\frac{1}{5}} y ^{\frac{6}{5}}}{z ^{\frac{2}{5}}})^{5}

x^{2} (21 - 20 x) \leq 1

y^{2} - 3 y + 2 = 0

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