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

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

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

simplify

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

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the fraction rule:

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

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

Simplify

x (x + x^{- 1})^{- 1} : \frac{x ^{2}}{x ^{2} + 1}

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

Apply the fraction rule:

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

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

(- \frac{5}{2})^{2} + 5 (- \frac{5}{2}) + 6

4 x^{2} + 4 x - 15

3 + ∣ 2 + 5 x ∣ = 12

2 x + 9 \geq 7

x^{2} + 5 x - 10 = 0

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