$\begin{array}{l}\phantom{\phantom{;}3x\phantom{;}+1;}{\phantom{;}2x^{2}-3x\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{;}3x\phantom{;}+1\overline{\smash{)}\phantom{;}6x^{3}-7x^{2}\phantom{-;x^n}+2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}3x\phantom{;}+1;}\underline{-6x^{3}-2x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-6x^{3}-2x^{2};}-9x^{2}\phantom{-;x^n}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x\phantom{;}+1-;x^n;}\underline{\phantom{;}9x^{2}+3x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}9x^{2}+3x\phantom{;}-;x^n;}\phantom{;}3x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x\phantom{;}+1-;x^n-;x^n;}\underline{-3x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{;;-3x\phantom{;}-1\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}1\phantom{;}\phantom{;}\\\end{array}$

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