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