What is (x^{-1})/(x^{-2)+y^{-4}} ?

The solution to (x^{-1})/(x^{-2)+y^{-4}} is (xy^4)/(y^4+x^2)

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simplify (x^{-1})/(x^{-2)+y^{-4}}

simplify

\frac{x ^{- 1}}{x ^{- 2} + y ^{- 4}}

\frac{x y ^{4}}{y ^{4} + x ^{2}}

Solution steps

\frac{x ^{- 1}}{x ^{- 2} + y ^{- 4}}

Apply exponent rule:

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

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

= \frac{\frac{1}{x}}{x ^{- 2} + y ^{- 4}}

Simplify

x^{- 2} + y^{- 4} : \frac{y ^{4} + x ^{2}}{x ^{2} y ^{4}}

= \frac{\frac{1}{x}}{\frac{y ^{4} + x ^{2}}{x ^{2} y ^{4}}}

Apply the fraction rule:

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

= \frac{1 \cdot x ^{2} y ^{4}}{x ( y ^{4} + x ^{2} )}

Cancel

\frac{1 \cdot x ^{2} y ^{4}}{x ( y ^{4} + x ^{2} )} : \frac{x y ^{4}}{y ^{4} + x ^{2}}

= \frac{x y ^{4}}{y ^{4} + x ^{2}}

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x^{2} y + x^{4} y^{4}

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\frac{( 1 - x ^{2} ) ( 2 - x )}{x ^{2} + 5 x + 6} \leq 0

What is (x^{-1})/(x^{-2)+y^{-4}} ?
The solution to (x^{-1})/(x^{-2)+y^{-4}} is (xy^4)/(y^4+x^2)