$\begin{array}{l}\phantom{\phantom{;}z^{2}-z\phantom{;}+1;}{\phantom{;}1\phantom{;}\phantom{;}}\\\phantom{;}z^{2}-z\phantom{;}+1\overline{\smash{)}\phantom{;}z^{2}+z\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}z^{2}-z\phantom{;}+1;}\underline{-z^{2}+z\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{-z^{2}+z\phantom{;}-1\phantom{;}\phantom{;};}\phantom{;}2z\phantom{;}-2\phantom{;}\phantom{;}\\\end{array}$

$1+\frac{2z-2}{z^2-z+1}$