$\begin{array}{l}\phantom{\phantom{;}3x\phantom{;}-2;}{\phantom{;}2x^{2}+5x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{;}3x\phantom{;}-2\overline{\smash{)}\phantom{;}6x^{3}+11x^{2}-x\phantom{;}-2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}3x\phantom{;}-2;}\underline{-6x^{3}+4x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-6x^{3}+4x^{2};}\phantom{;}15x^{2}-x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x\phantom{;}-2-;x^n;}\underline{-15x^{2}+10x\phantom{;}\phantom{-;x^n}}\\\phantom{;-15x^{2}+10x\phantom{;}-;x^n;}\phantom{;}9x\phantom{;}-2\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x\phantom{;}-2-;x^n-;x^n;}\underline{-9x\phantom{;}+6\phantom{;}\phantom{;}}\\\phantom{;;-9x\phantom{;}+6\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}4\phantom{;}\phantom{;}\\\end{array}$

$2x^{2}+5x+3+\frac{4}{3x-2}$