$\begin{array}{l}\phantom{\phantom{;}x^{2}+x\phantom{;}+4;}{\phantom{;}x^{2}-x\phantom{;}-3\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+x\phantom{;}+4\overline{\smash{)}\phantom{;}x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+x\phantom{;}+4;}\underline{-x^{4}-x^{3}-4x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}-x^{3}-4x^{2};}-x^{3}-4x^{2}\phantom{-;x^n}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+x\phantom{;}+4-;x^n;}\underline{\phantom{;}x^{3}+x^{2}+4x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}x^{3}+x^{2}+4x\phantom{;}-;x^n;}-3x^{2}+4x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+x\phantom{;}+4-;x^n-;x^n;}\underline{\phantom{;}3x^{2}+3x\phantom{;}+12\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}3x^{2}+3x\phantom{;}+12\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}7x\phantom{;}+14\phantom{;}\phantom{;}\\\end{array}$

$x^{2}-x-3+\frac{7x+14}{x^2+x+4}$