1. ## Division Review Problem

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:

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

2. ## Re: Division Review Problem

When you flipped the fraction in the denominator, you can cancel both terms out. Try factoring the numerator at this step (a difference of squares):
$\displaystyle \frac{y^2-1}{y}*\frac{y}{y-1}$

3. ## Re: Division Review Problem

I would simply multiply the fraction by $\displaystyle 1=\frac{y}{y}$:

$\displaystyle \frac{y-\frac{1}{y}}{1-\frac{1}{y}}\cdot\frac{y}{y}=\frac{y^2-1}{y-1}=\frac{(y+1)(y-1)}{y-1}=y+1$

4. ## Re: Division Review Problem

oh that's right, thanks a lot. I always miss those because at first glance it looks prime.