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

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