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Popular >

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

Solution

simplify

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

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

Join

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

= \frac{1}{\frac{x ^{2} + 1}{x}}

Apply the fraction rule:

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

= \frac{x}{x ^{2} + 1}

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Frequently Asked Questions (FAQ)

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