$\begin{array}{l}\phantom{\phantom{;}x^{2}+1;}{\phantom{;}32x^{3}-x^{2}-32x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+1\overline{\smash{)}\phantom{;}32x^{5}-x^{4}\phantom{-;x^n}+x^{2}\phantom{-;x^n}-2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+1;}\underline{-32x^{5}\phantom{-;x^n}-32x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-32x^{5}-32x^{3};}-x^{4}-32x^{3}+x^{2}\phantom{-;x^n}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+1-;x^n;}\underline{\phantom{;}x^{4}\phantom{-;x^n}+x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}x^{4}+x^{2}-;x^n;}-32x^{3}+2x^{2}\phantom{-;x^n}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+1-;x^n-;x^n;}\underline{\phantom{;}32x^{3}\phantom{-;x^n}+32x\phantom{;}\phantom{-;x^n}}\\\phantom{;;\phantom{;}32x^{3}+32x\phantom{;}-;x^n-;x^n;}\phantom{;}2x^{2}+32x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+1-;x^n-;x^n-;x^n;}\underline{-2x^{2}\phantom{-;x^n}-2\phantom{;}\phantom{;}}\\\phantom{;;;-2x^{2}-2\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}\phantom{;}32x\phantom{;}-4\phantom{;}\phantom{;}\\\end{array}$

$32x^{3}-x^{2}-32x+2+\frac{32x-4}{x^2+1}$