# Rational expressions

• Sep 29th 2009, 12:13 PM
Rheanna
Rational expressions
I've been looking at the examples in the book and can't find any examples on similar to this problem and I'm trying to figure out how I would go about solving it. Thank You

r- r^2-1/r / 1- r-1/r everything is all divided but I don't know how to write the tags in format.
• Sep 29th 2009, 12:38 PM
masters
Quote:

Originally Posted by Rheanna
I've been looking at the examples in the book and can't find any examples on similar to this problem and I'm trying to figure out how I would go about solving it. Thank You

r- r^2-1/r / 1- r-1/r everything is all divided but I don't know how to write the tags in format.

Hi Rheanna,

Parentheses might help. Is this your rational expression?

$\displaystyle \dfrac{r-r^2-\dfrac{1}{r}}{1-r-\dfrac{1}{r}}$
• Sep 29th 2009, 12:46 PM
Rheanna
Quote:

Originally Posted by masters
Hi Rheanna,

Parentheses might help. Is this your rational expression?

$\displaystyle \dfrac{r-r^2-\dfrac{1}{r}}{1-r-\dfrac{1}{r}}$

top one is r square 2-1/r
bottom one is r-1/r

it comes out to 1 as the answer but i'm trying to figure out how to come up with that.
• Sep 29th 2009, 12:50 PM
masters
Quote:

Originally Posted by masters
Hi Rheanna,

Parentheses might help. Is this your rational expression?

$\displaystyle \dfrac{r-r^2-\dfrac{1}{r}}{1-r-\dfrac{1}{r}}$

Quote:

Originally Posted by Rheanna
top one is r square 2-1/r
bottom one is r-1/r

You mean like this:

$\displaystyle \dfrac{r-\dfrac{r^2-1}{r}}{1-\dfrac{r-1}{r}}$
• Sep 29th 2009, 01:00 PM
Rheanna
yes :)
• Sep 29th 2009, 01:11 PM
masters
Quote:

Originally Posted by masters
You mean like this:

$\displaystyle \dfrac{r-\dfrac{r^2-1}{r}}{1-\dfrac{r-1}{r}}$

Alrighty then,

$\displaystyle \dfrac{r-\dfrac{r^2-1}{r}}{1-\dfrac{r-1}{r}}=\dfrac{\dfrac{r^2-(r^2-1)}{r}}{\dfrac{r-(r-1)}{r}}=\dfrac{\dfrac{r^2-r^2+1}{r}}{\dfrac{r-r+1}{r}}=\dfrac{\dfrac{1}{r}}{\dfrac{1}{r}}=1$
• Sep 29th 2009, 01:17 PM
Rheanna
lol, even staring at the problem i'm still lost. :)(Thinking)
• Sep 29th 2009, 01:38 PM
masters
Quote:

Originally Posted by masters
Alrighty then,

$\displaystyle \dfrac{r-\dfrac{r^2-1}{r}}{1-\dfrac{r-1}{r}}=\dfrac{\dfrac{r^2-(r^2-1)}{r}}{\dfrac{r-(r-1)}{r}}=\dfrac{\dfrac{r^2-r^2+1}{r}}{\dfrac{r-r+1}{r}}=\dfrac{\dfrac{1}{r}}{\dfrac{1}{r}}=1$

Let me do it another way. See if this helps.

Multiply numerator and denominator by r.

$\displaystyle \dfrac{r-\dfrac{r^2-1}{r}}{1-\dfrac{r-1}{r}}$

$\displaystyle \dfrac{r\left(r-\dfrac{r^2-1}{r}\right)}{r\left(1-\dfrac{r-1}{r}\right)}=\dfrac{r^2-r^2+1}{r-r+1}=\frac{1}{1}=1$
• Sep 29th 2009, 03:51 PM
Rheanna
yeah that r square was confusing me. (Itwasntme) ugh I know I got 0 on this pre test and Thursday is the test test. (Crying)