What is (x^{-1})/(x^{-2)+y^{-6}} ?

The solution to (x^{-1})/(x^{-2)+y^{-6}} is (xy^6)/(y^6+x^2)

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simplify (x^{-1})/(x^{-2)+y^{-6}}

simplify

\frac{x ^{- 1}}{x ^{- 2} + y ^{- 6}}

\frac{x y ^{6}}{y ^{6} + x ^{2}}

Solution steps

\frac{x ^{- 1}}{x ^{- 2} + y ^{- 6}}

Apply exponent rule:

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

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

= \frac{\frac{1}{x}}{x ^{- 2} + y ^{- 6}}

Simplify

x^{- 2} + y^{- 6} : \frac{y ^{6} + x ^{2}}{x ^{2} y ^{6}}

= \frac{\frac{1}{x}}{\frac{y ^{6} + x ^{2}}{x ^{2} y ^{6}}}

Apply the fraction rule:

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

= \frac{1 \cdot x ^{2} y ^{6}}{x ( y ^{6} + x ^{2} )}

Cancel

\frac{1 \cdot x ^{2} y ^{6}}{x ( y ^{6} + x ^{2} )} : \frac{x y ^{6}}{y ^{6} + x ^{2}}

= \frac{x y ^{6}}{y ^{6} + x ^{2}}

5 x + 5 > 2 x + 2

9^{\frac{1}{3}} \cdot 8 1^{\frac{1}{3}}

y + 5 > 9

2 2^{2} - 121 = 11

x^{2} + 14 x + 65 = 0

What is (x^{-1})/(x^{-2)+y^{-6}} ?
The solution to (x^{-1})/(x^{-2)+y^{-6}} is (xy^6)/(y^6+x^2)