$\begin{array}{l}\phantom{\phantom{;}a^{2}-3a\phantom{;}+3;}{\phantom{;}3a^{2}+14a\phantom{;}+33\phantom{;}\phantom{;}}\\\phantom{;}a^{2}-3a\phantom{;}+3\overline{\smash{)}\phantom{;}3a^{4}+5a^{3}\phantom{-;x^n}-2a\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}a^{2}-3a\phantom{;}+3;}\underline{-3a^{4}+9a^{3}-9a^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3a^{4}+9a^{3}-9a^{2};}\phantom{;}14a^{3}-9a^{2}-2a\phantom{;}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}a^{2}-3a\phantom{;}+3-;x^n;}\underline{-14a^{3}+42a^{2}-42a\phantom{;}\phantom{-;x^n}}\\\phantom{;-14a^{3}+42a^{2}-42a\phantom{;}-;x^n;}\phantom{;}33a^{2}-44a\phantom{;}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}a^{2}-3a\phantom{;}+3-;x^n-;x^n;}\underline{-33a^{2}+99a\phantom{;}-99\phantom{;}\phantom{;}}\\\phantom{;;-33a^{2}+99a\phantom{;}-99\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}55a\phantom{;}-96\phantom{;}\phantom{;}\\\end{array}$

$3a^{2}+14a+33+\frac{55a-96}{a^2-3a+3}$