$\begin{array}{l}\phantom{\phantom{;}4x\phantom{;}-1;}{\phantom{;}2x^{2}+2x\phantom{;}+5\phantom{;}\phantom{;}}\\\phantom{;}4x\phantom{;}-1\overline{\smash{)}\phantom{;}8x^{3}+6x^{2}+18x\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}4x\phantom{;}-1;}\underline{-8x^{3}+2x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-8x^{3}+2x^{2};}\phantom{;}8x^{2}+18x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}4x\phantom{;}-1-;x^n;}\underline{-8x^{2}+2x\phantom{;}\phantom{-;x^n}}\\\phantom{;-8x^{2}+2x\phantom{;}-;x^n;}\phantom{;}20x\phantom{;}+1\phantom{;}\phantom{;}\\\phantom{\phantom{;}4x\phantom{;}-1-;x^n-;x^n;}\underline{-20x\phantom{;}+5\phantom{;}\phantom{;}}\\\phantom{;;-20x\phantom{;}+5\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}6\phantom{;}\phantom{;}\\\end{array}$

$2x^{2}+2x+5+\frac{6}{4x-1}$