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

The solution to (x+x^{-2})/(1+x^{-2)} is (x^3+1)/(x^2+1)

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

simplify

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

\frac{x ^{3} + 1}{x ^{2} + 1}

Solution steps

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

Simplify

x + x^{- 2} : \frac{x ^{3} + 1}{x ^{2}}

= \frac{\frac{x ^{3} + 1}{x ^{2}}}{1 + x ^{- 2}}

Simplify

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

= \frac{\frac{x ^{3} + 1}{x ^{2}}}{\frac{x ^{2} + 1}{x ^{2}}}

Apply the fraction rule:

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

= \frac{( x ^{3} + 1 ) x ^{2}}{x ^{2} ( x ^{2} + 1 )}

Cancel the common factor:

x^{2}

= \frac{x ^{3} + 1}{x ^{2} + 1}

x^{3} - 2 x^{2} - 6 x + 12

\frac{5 i}{6 - 2 i}

(- 4 - 4 i)^{2}

7.2 x^{2} y - 0.9 x y^{2}

\frac{7}{20} - \frac{3}{8}

What is (x+x^{-2})/(1+x^{-2)} ?
The solution to (x+x^{-2})/(1+x^{-2)} is (x^3+1)/(x^2+1)