$\begin{array}{l}\phantom{\phantom{;}2x\phantom{;}-1;}{\phantom{;}2x^{2}+x\phantom{;}+4\phantom{;}\phantom{;}}\\\phantom{;}2x\phantom{;}-1\overline{\smash{)}\phantom{;}4x^{3}\phantom{-;x^n}+7x\phantom{;}+9\phantom{;}\phantom{;}}\\\phantom{\phantom{;}2x\phantom{;}-1;}\underline{-4x^{3}+2x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-4x^{3}+2x^{2};}\phantom{;}2x^{2}+7x\phantom{;}+9\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x\phantom{;}-1-;x^n;}\underline{-2x^{2}+x\phantom{;}\phantom{-;x^n}}\\\phantom{;-2x^{2}+x\phantom{;}-;x^n;}\phantom{;}8x\phantom{;}+9\phantom{;}\phantom{;}\\\phantom{\phantom{;}2x\phantom{;}-1-;x^n-;x^n;}\underline{-8x\phantom{;}+4\phantom{;}\phantom{;}}\\\phantom{;;-8x\phantom{;}+4\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}13\phantom{;}\phantom{;}\\\end{array}$

$2x^{2}+x+4+\frac{13}{2x-1}$