$\begin{array}{l}\phantom{\phantom{;}3x\phantom{;}-5;}{\phantom{;}2x^{2}+6x\phantom{;}-6\phantom{;}\phantom{;}}\\\phantom{;}3x\phantom{;}-5\overline{\smash{)}\phantom{;}6x^{3}+8x^{2}-48x\phantom{;}+21\phantom{;}\phantom{;}}\\\phantom{\phantom{;}3x\phantom{;}-5;}\underline{-6x^{3}+10x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-6x^{3}+10x^{2};}\phantom{;}18x^{2}-48x\phantom{;}+21\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x\phantom{;}-5-;x^n;}\underline{-18x^{2}+30x\phantom{;}\phantom{-;x^n}}\\\phantom{;-18x^{2}+30x\phantom{;}-;x^n;}-18x\phantom{;}+21\phantom{;}\phantom{;}\\\phantom{\phantom{;}3x\phantom{;}-5-;x^n-;x^n;}\underline{\phantom{;}18x\phantom{;}-30\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}18x\phantom{;}-30\phantom{;}\phantom{;}-;x^n-;x^n;}-9\phantom{;}\phantom{;}\\\end{array}$

$2x^{2}+6x-6+\frac{-9}{3x-5}$