$\begin{array}{l}\phantom{\phantom{;}v\phantom{;}-3;}{\phantom{;}v^{2}-3v\phantom{;}-9\phantom{;}\phantom{;}}\\\phantom{;}v\phantom{;}-3\overline{\smash{)}\phantom{;}v^{3}-6v^{2}\phantom{-;x^n}+3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}v\phantom{;}-3;}\underline{-v^{3}+3v^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-v^{3}+3v^{2};}-3v^{2}\phantom{-;x^n}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}v\phantom{;}-3-;x^n;}\underline{\phantom{;}3v^{2}-9v\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}3v^{2}-9v\phantom{;}-;x^n;}-9v\phantom{;}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}v\phantom{;}-3-;x^n-;x^n;}\underline{\phantom{;}9v\phantom{;}-27\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}9v\phantom{;}-27\phantom{;}\phantom{;}-;x^n-;x^n;}-24\phantom{;}\phantom{;}\\\end{array}$

$v^{2}-3v-9+\frac{-24}{v-3}$