$\begin{array}{l}\phantom{\phantom{;}2x\phantom{;}+3;}{\phantom{;}3x^{2}-6x\phantom{;}+9\phantom{;}\phantom{;}}\\\phantom{;}2x\phantom{;}+3\overline{\smash{)}\phantom{;}6x^{3}-3x^{2}\phantom{-;x^n}-8\phantom{;}\phantom{;}}\\\phantom{\phantom{;}2x\phantom{;}+3;}\underline{-6x^{3}-9x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-6x^{3}-9x^{2};}-12x^{2}\phantom{-;x^n}-8\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x\phantom{;}+3-;x^n;}\underline{\phantom{;}12x^{2}+18x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}12x^{2}+18x\phantom{;}-;x^n;}\phantom{;}18x\phantom{;}-8\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x\phantom{;}+3-;x^n-;x^n;}\underline{-18x\phantom{;}-27\phantom{;}\phantom{;}}\\\phantom{;;-18x\phantom{;}-27\phantom{;}\phantom{;}-;x^n-;x^n;}-35\phantom{;}\phantom{;}\\\end{array}$

$3x^{2}-6x+9+\frac{-35}{2x+3}$