$\begin{array}{l}\phantom{\phantom{;}2x^{3}+x\phantom{;}-1;}{\phantom{;}3x^{2}+2x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{;}2x^{3}+x\phantom{;}-1\overline{\smash{)}\phantom{;}6x^{5}+4x^{4}+9x^{3}\phantom{-;x^n}\phantom{-;x^n}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}2x^{3}+x\phantom{;}-1;}\underline{-6x^{5}\phantom{-;x^n}-3x^{3}+3x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-6x^{5}-3x^{3}+3x^{2};}\phantom{;}4x^{4}+6x^{3}+3x^{2}\phantom{-;x^n}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x^{3}+x\phantom{;}-1-;x^n;}\underline{-4x^{4}\phantom{-;x^n}-2x^{2}+2x\phantom{;}\phantom{-;x^n}}\\\phantom{;-4x^{4}-2x^{2}+2x\phantom{;}-;x^n;}\phantom{;}6x^{3}+x^{2}+2x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x^{3}+x\phantom{;}-1-;x^n-;x^n;}\underline{-6x^{3}\phantom{-;x^n}-3x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{;;-6x^{3}-3x\phantom{;}+3\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}x^{2}-x\phantom{;}+2\phantom{;}\phantom{;}\\\end{array}$

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