$\begin{array}{l}\phantom{\phantom{;}x^{2}+3x\phantom{;}+0.5;}{\phantom{;}x^{2}-3x\phantom{;}+8.5\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+3x\phantom{;}+0.5\overline{\smash{)}\phantom{;}x^{4}\phantom{-;x^n}\phantom{-;x^n}+6x\phantom{;}-2.5\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+3x\phantom{;}+0.5;}\underline{-x^{4}-3x^{3}-0.5x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}-3x^{3}-0.5x^{2};}-3x^{3}-0.5x^{2}+6x\phantom{;}-2.5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+3x\phantom{;}+0.5-;x^n;}\underline{\phantom{;}3x^{3}+9x^{2}+1.5x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}3x^{3}+9x^{2}+1.5x\phantom{;}-;x^n;}\phantom{;}8.5x^{2}+7.5x\phantom{;}-2.5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+3x\phantom{;}+0.5-;x^n-;x^n;}\underline{-8.5x^{2}-25.5x\phantom{;}-4.25\phantom{;}\phantom{;}}\\\phantom{;;-8.5x^{2}-25.5x\phantom{;}-4.25\phantom{;}\phantom{;}-;x^n-;x^n;}-18x\phantom{;}-6.75\phantom{;}\phantom{;}\\\end{array}$

$x^{2}-3x+8.5+\frac{-18x-6.75}{x^2+3x+0.5}$