Answer
$\displaystyle \frac{y}{3}$
Work Step by Step
Dividing with $\displaystyle \frac{P}{Q}$ equals multiplying with the reciprocal, $\displaystyle \frac{Q}{P}.$
$ \displaystyle \frac{y^{2}-y}{15}\div\frac{y-1}{5}=\frac{y^{2}-y}{15}\cdot\frac{5}{y-1}\qquad$... factor what you can
$=\displaystyle \frac{y(y-1)}{15}\cdot\frac{5}{(y-1)}\qquad$... divide out the common factors
$=\displaystyle \frac{y(1)}{3}\cdot\frac{1}{(1)}$
= $\displaystyle \frac{y}{3}$
