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

$4x^{2}-3x+1+\frac{5}{2x-1}$