$\begin{array}{l}\phantom{\phantom{;}a\phantom{;}-2;}{\phantom{;}a^{2}-a\phantom{;}-3\phantom{;}\phantom{;}}\\\phantom{;}a\phantom{;}-2\overline{\smash{)}\phantom{;}a^{3}-3a^{2}-a\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}a\phantom{;}-2;}\underline{-a^{3}+2a^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-a^{3}+2a^{2};}-a^{2}-a\phantom{;}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}a\phantom{;}-2-;x^n;}\underline{\phantom{;}a^{2}-2a\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}a^{2}-2a\phantom{;}-;x^n;}-3a\phantom{;}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}a\phantom{;}-2-;x^n-;x^n;}\underline{\phantom{;}3a\phantom{;}-6\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}3a\phantom{;}-6\phantom{;}\phantom{;}-;x^n-;x^n;}-3\phantom{;}\phantom{;}\\\end{array}$

$a^{2}-a-3+\frac{-3}{a-2}$