$\begin{array}{l}\phantom{\phantom{;}x^{2}-3;}{\phantom{;}5x^{3}\phantom{-;x^n}+11x\phantom{;}\phantom{-;x^n}}\\\phantom{;}x^{2}-3\overline{\smash{)}\phantom{;}5x^{5}\phantom{-;x^n}-4x^{3}\phantom{-;x^n}-3x\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-3;}\underline{-5x^{5}\phantom{-;x^n}+15x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-5x^{5}+15x^{3};}\phantom{;}11x^{3}\phantom{-;x^n}-3x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-3-;x^n;}\underline{-11x^{3}\phantom{-;x^n}+33x\phantom{;}\phantom{-;x^n}}\\\phantom{;-11x^{3}+33x\phantom{;}-;x^n;}\phantom{;}30x\phantom{;}+1\phantom{;}\phantom{;}\\\end{array}$

$5x^{3}+11x+\frac{30x+1}{x^2-3}$