$\begin{array}{l}\phantom{\phantom{;}x^{2}+3;}{\phantom{;}x^{2}-x\phantom{;}-3\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+3\overline{\smash{)}\phantom{;}x^{4}-x^{3}\phantom{-;x^n}+4x\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+3;}\underline{-x^{4}\phantom{-;x^n}-3x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}-3x^{2};}-x^{3}-3x^{2}+4x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+3-;x^n;}\underline{\phantom{;}x^{3}\phantom{-;x^n}+3x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}x^{3}+3x\phantom{;}-;x^n;}-3x^{2}+7x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+3-;x^n-;x^n;}\underline{\phantom{;}3x^{2}\phantom{-;x^n}+9\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}3x^{2}+9\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}7x\phantom{;}+10\phantom{;}\phantom{;}\\\end{array}$

$x^{2}-x-3+\frac{7x+10}{x^2+3}$