Final answer to the problem
$x+\frac{x}{x^2-1}$
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1
Divide $x^3$ by $x^2-1$
$\begin{array}{l}\phantom{\phantom{;}x^{2}-1;}{\phantom{;}x\phantom{;}\phantom{-;x^n}}\\\phantom{;}x^{2}-1\overline{\smash{)}\phantom{;}x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}x^{2}-1;}\underline{-x^{3}\phantom{-;x^n}+x\phantom{;}\phantom{-;x^n}}\\\phantom{-x^{3}+x\phantom{;};}\phantom{;}x\phantom{;}\phantom{-;x^n}\\\end{array}$
2
Resulting polynomial
$x+\frac{x}{x^2-1}$
Final answer to the problem
$x+\frac{x}{x^2-1}$
