$\begin{array}{l}\phantom{\phantom{;}3x\phantom{;}-1;}{\phantom{;}2x^{4}+x^{3}+3x^{2}+x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{;}3x\phantom{;}-1\overline{\smash{)}\phantom{;}6x^{5}+x^{4}+8x^{3}\phantom{-;x^n}-4x\phantom{;}+8\phantom{;}\phantom{;}}\\\phantom{\phantom{;}3x\phantom{;}-1;}\underline{-6x^{5}+2x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-6x^{5}+2x^{4};}\phantom{;}3x^{4}+8x^{3}\phantom{-;x^n}-4x\phantom{;}+8\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x\phantom{;}-1-;x^n;}\underline{-3x^{4}+x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-3x^{4}+x^{3}-;x^n;}\phantom{;}9x^{3}\phantom{-;x^n}-4x\phantom{;}+8\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x\phantom{;}-1-;x^n-;x^n;}\underline{-9x^{3}+3x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;;-9x^{3}+3x^{2}-;x^n-;x^n;}\phantom{;}3x^{2}-4x\phantom{;}+8\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x\phantom{;}-1-;x^n-;x^n-;x^n;}\underline{-3x^{2}+x\phantom{;}\phantom{-;x^n}}\\\phantom{;;;-3x^{2}+x\phantom{;}-;x^n-;x^n-;x^n;}-3x\phantom{;}+8\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x\phantom{;}-1-;x^n-;x^n-;x^n-;x^n;}\underline{\phantom{;}3x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{;;;;\phantom{;}3x\phantom{;}-1\phantom{;}\phantom{;}-;x^n-;x^n-;x^n-;x^n;}\phantom{;}7\phantom{;}\phantom{;}\\\end{array}$

$2x^{4}+x^{3}+3x^{2}+x-1+\frac{7}{3x-1}$