$\begin{array}{l}\phantom{\phantom{;}x^{2}-3;}{\phantom{;}5x^{2}+x\phantom{;}+15\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-3\overline{\smash{)}\phantom{;}5x^{4}+x^{3}\phantom{-;x^n}+5x\phantom{;}-14\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-3;}\underline{-5x^{4}\phantom{-;x^n}+15x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-5x^{4}+15x^{2};}\phantom{;}x^{3}+15x^{2}+5x\phantom{;}-14\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-3-;x^n;}\underline{-x^{3}\phantom{-;x^n}+3x\phantom{;}\phantom{-;x^n}}\\\phantom{;-x^{3}+3x\phantom{;}-;x^n;}\phantom{;}15x^{2}+8x\phantom{;}-14\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-3-;x^n-;x^n;}\underline{-15x^{2}\phantom{-;x^n}+45\phantom{;}\phantom{;}}\\\phantom{;;-15x^{2}+45\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}8x\phantom{;}+31\phantom{;}\phantom{;}\\\end{array}$

$5x^{2}+x+15+\frac{8x+31}{x^2-3}$