$\begin{array}{l}\phantom{\phantom{;}3x\phantom{;}-2;}{\phantom{;}x^{3}+3x^{2}+x\phantom{;}+4\phantom{;}\phantom{;}}\\\phantom{;}3x\phantom{;}-2\overline{\smash{)}\phantom{;}3x^{4}+7x^{3}-3x^{2}+10x\phantom{;}-19\phantom{;}\phantom{;}}\\\phantom{\phantom{;}3x\phantom{;}-2;}\underline{-3x^{4}+2x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{4}+2x^{3};}\phantom{;}9x^{3}-3x^{2}+10x\phantom{;}-19\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x\phantom{;}-2-;x^n;}\underline{-9x^{3}+6x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-9x^{3}+6x^{2}-;x^n;}\phantom{;}3x^{2}+10x\phantom{;}-19\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x\phantom{;}-2-;x^n-;x^n;}\underline{-3x^{2}+2x\phantom{;}\phantom{-;x^n}}\\\phantom{;;-3x^{2}+2x\phantom{;}-;x^n-;x^n;}\phantom{;}12x\phantom{;}-19\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x\phantom{;}-2-;x^n-;x^n-;x^n;}\underline{-12x\phantom{;}+8\phantom{;}\phantom{;}}\\\phantom{;;;-12x\phantom{;}+8\phantom{;}\phantom{;}-;x^n-;x^n-;x^n;}-11\phantom{;}\phantom{;}\\\end{array}$

$x^{3}+3x^{2}+x+4+\frac{-11}{3x-2}$