$\begin{array}{l}\phantom{\phantom{;}x^{2}+3x\phantom{;}+4;}{\phantom{;}x^{2}-3x\phantom{;}+5\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+3x\phantom{;}+4\overline{\smash{)}\phantom{;}x^{4}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+3x\phantom{;}+4;}\underline{-x^{4}-3x^{3}-4x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}-3x^{3}-4x^{2};}-3x^{3}-4x^{2}\phantom{-;x^n}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+3x\phantom{;}+4-;x^n;}\underline{\phantom{;}3x^{3}+9x^{2}+12x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}3x^{3}+9x^{2}+12x\phantom{;}-;x^n;}\phantom{;}5x^{2}+12x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+3x\phantom{;}+4-;x^n-;x^n;}\underline{-5x^{2}-15x\phantom{;}-20\phantom{;}\phantom{;}}\\\phantom{;;-5x^{2}-15x\phantom{;}-20\phantom{;}\phantom{;}-;x^n-;x^n;}-3x\phantom{;}-18\phantom{;}\phantom{;}\\\end{array}$

$x^{2}-3x+5+\frac{-3x-18}{x^2+3x+4}$