Answer
$\frac{z-1}{z^2+2}$.
Work Step by Step
The given expression is
$=\frac{z^2-2z+1}{z^2+2}\div (z-1)$
Factor.
$=\frac{(z-1)(z-1)}{z^2+2}\div (z-1)$
$=\frac{(z-1)(z-1)}{z^2+2}\times \frac{1}{z-1}$
Divide out the common factors.
$=\frac{z-1}{z^2+2}$.
