Hello all, I was doing some review of complex fractions but I am not sure if I did this one right, please let me know if, or where, I went wrong. I also wanted to practice using latex some more. Thanks!

Reduce to lowest terms:

$\displaystyle \frac{y-\frac{1}{y}}{1-\frac{1}{y}}$ = $\displaystyle \frac{\frac{y^2-1}{y}}{\frac{y-1}{y}}$ = $\displaystyle \frac{y^2-1}{y}*\frac{y}{y-1}$ = $\displaystyle \frac{y^3-y}{y^2-y}$