$\begin{array}{l}\phantom{\phantom{;}2x\phantom{;}-1;}{\phantom{;}3x^{2}-x\phantom{;}+4\phantom{;}\phantom{;}}\\\phantom{;}2x\phantom{;}-1\overline{\smash{)}\phantom{;}6x^{3}-5x^{2}+9x\phantom{;}+6\phantom{;}\phantom{;}}\\\phantom{\phantom{;}2x\phantom{;}-1;}\underline{-6x^{3}+3x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-6x^{3}+3x^{2};}-2x^{2}+9x\phantom{;}+6\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x\phantom{;}-1-;x^n;}\underline{\phantom{;}2x^{2}-x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}2x^{2}-x\phantom{;}-;x^n;}\phantom{;}8x\phantom{;}+6\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x\phantom{;}-1-;x^n-;x^n;}\underline{-8x\phantom{;}+4\phantom{;}\phantom{;}}\\\phantom{;;-8x\phantom{;}+4\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}10\phantom{;}\phantom{;}\\\end{array}$

$3x^{2}-x+4+\frac{10}{2x-1}$