$\begin{array}{l}\phantom{\phantom{;}x^{2}+8x\phantom{;}+6;}{\phantom{;}5x\phantom{;}-37\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+8x\phantom{;}+6\overline{\smash{)}\phantom{;}5x^{3}+3x^{2}-6x\phantom{;}+8\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+8x\phantom{;}+6;}\underline{-5x^{3}-40x^{2}-30x\phantom{;}\phantom{-;x^n}}\\\phantom{-5x^{3}-40x^{2}-30x\phantom{;};}-37x^{2}-36x\phantom{;}+8\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+8x\phantom{;}+6-;x^n;}\underline{\phantom{;}37x^{2}+296x\phantom{;}+222\phantom{;}\phantom{;}}\\\phantom{;\phantom{;}37x^{2}+296x\phantom{;}+222\phantom{;}\phantom{;}-;x^n;}\phantom{;}260x\phantom{;}+230\phantom{;}\phantom{;}\\\end{array}$

$5x-37+\frac{260x+230}{x^2+8x+6}$