$\begin{array}{l}\phantom{\phantom{;}x^{2}+3;}{\phantom{;}3x^{2}-4x\phantom{;}-9\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+3\overline{\smash{)}\phantom{;}3x^{4}-4x^{3}\phantom{-;x^n}+5x\phantom{;}-12\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+3;}\underline{-3x^{4}\phantom{-;x^n}-9x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-3x^{4}-9x^{2};}-4x^{3}-9x^{2}+5x\phantom{;}-12\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+3-;x^n;}\underline{\phantom{;}4x^{3}\phantom{-;x^n}+12x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}4x^{3}+12x\phantom{;}-;x^n;}-9x^{2}+17x\phantom{;}-12\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+3-;x^n-;x^n;}\underline{\phantom{;}9x^{2}\phantom{-;x^n}+27\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}9x^{2}+27\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}17x\phantom{;}+15\phantom{;}\phantom{;}\\\end{array}$

$3x^{2}-4x-9+\frac{17x+15}{x^2+3}$