$\begin{array}{l}\phantom{\phantom{;}3x\phantom{;}-1;}{\phantom{;}9x^{3}+3x^{2}-x\phantom{;}\phantom{-;x^n}}\\\phantom{;}3x\phantom{;}-1\overline{\smash{)}\phantom{;}27x^{4}\phantom{-;x^n}-6x^{2}+x\phantom{;}+15\phantom{;}\phantom{;}}\\\phantom{\phantom{;}3x\phantom{;}-1;}\underline{-27x^{4}+9x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-27x^{4}+9x^{3};}\phantom{;}9x^{3}-6x^{2}+x\phantom{;}+15\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x\phantom{;}-1-;x^n;}\underline{-9x^{3}+3x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{;-9x^{3}+3x^{2}-;x^n;}-3x^{2}+x\phantom{;}+15\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x\phantom{;}-1-;x^n-;x^n;}\underline{\phantom{;}3x^{2}-x\phantom{;}\phantom{-;x^n}}\\\phantom{;;\phantom{;}3x^{2}-x\phantom{;}-;x^n-;x^n;}\phantom{;}15\phantom{;}\phantom{;}\\\end{array}$

$9x^{3}+3x^{2}-x+\frac{15}{3x-1}$