$\begin{array}{l}\phantom{\phantom{;}x^{2}+3x\phantom{;}-1;}{\phantom{;}5x\phantom{;}-15\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+3x\phantom{;}-1\overline{\smash{)}\phantom{;}5x^{3}\phantom{-;x^n}-3x\phantom{;}+4\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+3x\phantom{;}-1;}\underline{-5x^{3}-15x^{2}+5x\phantom{;}\phantom{-;x^n}}\\\phantom{-5x^{3}-15x^{2}+5x\phantom{;};}-15x^{2}+2x\phantom{;}+4\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+3x\phantom{;}-1-;x^n;}\underline{\phantom{;}15x^{2}+45x\phantom{;}-15\phantom{;}\phantom{;}}\\\phantom{;\phantom{;}15x^{2}+45x\phantom{;}-15\phantom{;}\phantom{;}-;x^n;}\phantom{;}47x\phantom{;}-11\phantom{;}\phantom{;}\\\end{array}$

$5x-15+\frac{47x-11}{x^2+3x-1}$