Final Answer
$x+\frac{-x}{x^2+1}$
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Step-by-step Solution
Specify the solving method
1
Divide $x^3$ by $x^2+1$
$\begin{array}{l}\phantom{\phantom{;}x^{2}+1;}{\phantom{;}x\phantom{;}\phantom{-;x^n}}\\\phantom{;}x^{2}+1\overline{\smash{)}\phantom{;}x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}x^{2}+1;}\underline{-x^{3}\phantom{-;x^n}-x\phantom{;}\phantom{-;x^n}}\\\phantom{-x^{3}-x\phantom{;};}-x\phantom{;}\phantom{-;x^n}\\\end{array}$
2
Resulting polynomial
$x+\frac{-x}{x^2+1}$
Final Answer
$x+\frac{-x}{x^2+1}$