$\begin{array}{l}\phantom{\phantom{;}a^{2}+10a\phantom{;}-6;}{\phantom{;}1\phantom{;}\phantom{;}}\\\phantom{;}a^{2}+10a\phantom{;}-6\overline{\smash{)}\phantom{;}a^{2}-7a\phantom{;}+6\phantom{;}\phantom{;}}\\\phantom{\phantom{;}a^{2}+10a\phantom{;}-6;}\underline{-a^{2}-10a\phantom{;}+6\phantom{;}\phantom{;}}\\\phantom{-a^{2}-10a\phantom{;}+6\phantom{;}\phantom{;};}-17a\phantom{;}+12\phantom{;}\phantom{;}\\\end{array}$

$1+\frac{-17a+12}{a^2+10a-6}$