# Division Review Problem

• Jan 15th 2013, 06:01 PM
KhanDisciple
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:

$\displaystyle \frac{y-\frac{1}{y}}{1-\frac{1}{y}}$ = $\displaystyle \frac{\frac{y^2-1}{y}}{\frac{y-1}{y}}$ = $\displaystyle \frac{y^2-1}{y}*\frac{y}{y-1}$ = $\displaystyle \frac{y^3-y}{y^2-y}$
• Jan 15th 2013, 06:08 PM
divans
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):
$\displaystyle \frac{y^2-1}{y}*\frac{y}{y-1}$
• Jan 15th 2013, 06:31 PM
MarkFL
Re: Division Review Problem
I would simply multiply the fraction by $\displaystyle 1=\frac{y}{y}$:

$\displaystyle \frac{y-\frac{1}{y}}{1-\frac{1}{y}}\cdot\frac{y}{y}=\frac{y^2-1}{y-1}=\frac{(y+1)(y-1)}{y-1}=y+1$
• Jan 15th 2013, 06:47 PM
KhanDisciple
Re: Division Review Problem
oh that's right, thanks a lot. I always miss those because at first glance it looks prime.