$\begin{array}{l}\phantom{\phantom{;}3x^{2}-3x\phantom{;}-4;}{\phantom{;}x^{2}+x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{;}3x^{2}-3x\phantom{;}-4\overline{\smash{)}\phantom{;}3x^{4}\phantom{-;x^n}-x^{2}\phantom{-;x^n}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}3x^{2}-3x\phantom{;}-4;}\underline{-3x^{4}+3x^{3}+4x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{4}+3x^{3}+4x^{2};}\phantom{;}3x^{3}+3x^{2}\phantom{-;x^n}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x^{2}-3x\phantom{;}-4-;x^n;}\underline{-3x^{3}+3x^{2}+4x\phantom{;}\phantom{-;x^n}}\\\phantom{;-3x^{3}+3x^{2}+4x\phantom{;}-;x^n;}\phantom{;}6x^{2}+4x\phantom{;}-1\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x^{2}-3x\phantom{;}-4-;x^n-;x^n;}\underline{-6x^{2}+6x\phantom{;}+8\phantom{;}\phantom{;}}\\\phantom{;;-6x^{2}+6x\phantom{;}+8\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}10x\phantom{;}+7\phantom{;}\phantom{;}\\\end{array}$

$x^{2}+x+2+\frac{10x+7}{3x^2-3x-4}$