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Popular >

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

Solution

simplify

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

Solution

\frac{y}{x y + 1}

Solution steps

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

Apply exponent rule:

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

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

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

Apply exponent rule:

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

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

Join

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

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

Apply the fraction rule:

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

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

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Frequently Asked Questions (FAQ)

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