$\begin{array}{l}\phantom{\phantom{;}3x\phantom{;}+1;}{\phantom{;}2x^{3}-2x^{2}+x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{;}3x\phantom{;}+1\overline{\smash{)}\phantom{;}6x^{4}-4x^{3}+x^{2}+10x\phantom{;}-2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}3x\phantom{;}+1;}\underline{-6x^{4}-2x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-6x^{4}-2x^{3};}-6x^{3}+x^{2}+10x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x\phantom{;}+1-;x^n;}\underline{\phantom{;}6x^{3}+2x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;\phantom{;}6x^{3}+2x^{2}-;x^n;}\phantom{;}3x^{2}+10x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x\phantom{;}+1-;x^n-;x^n;}\underline{-3x^{2}-x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-3x^{2}-x\phantom{;}-;x^n-;x^n;}\phantom{;}9x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x\phantom{;}+1-;x^n-;x^n-;x^n;}\underline{-9x\phantom{;}-3\phantom{;}\phantom{;}}\\\phantom{;;;-9x\phantom{;}-3\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}-5\phantom{;}\phantom{;}\\\end{array}$

$2x^{3}-2x^{2}+x+3+\frac{-5}{3x+1}$