Final answer to the problem
$1+\frac{-1}{x^2+1}$
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1
Divide $x^2$ by $x^2+1$
$\begin{array}{l}\phantom{\phantom{;}x^{2}+1;}{\phantom{;}1\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+1\overline{\smash{)}\phantom{;}x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}x^{2}+1;}\underline{-x^{2}\phantom{-;x^n}-1\phantom{;}\phantom{;}}\\\phantom{-x^{2}-1\phantom{;}\phantom{;};}-1\phantom{;}\phantom{;}\\\end{array}$
2
Resulting polynomial
$1+\frac{-1}{x^2+1}$
Final answer to the problem
$1+\frac{-1}{x^2+1}$
