# Rational Expression With Two Variables

• Nov 19th 2012, 04:40 PM
zsf1990
Rational Expression With Two Variables
I'm a college student teaching himself algebra (loooong story) to save money on classes. I've done well so far, just finished up polynomials and now moving on to rational expressions. I've got the basics of factoring and writing in simplest terms down, but my book threw me a curveball:

Write in simplest terms:
9r2 - 4s2
-------
9r + 6s

I've factored it out to:

3r(3 + r) - 2s(2 + s)
----------
3(3 + r) + 3(2 + s)

Crossing out like terms, this leaves me with

3r-2s
-------
6

However, the book says the denominator should be 3, not 6. Knowing the answer doesn't do me any good if I don't understand how to get there. Where am I going wrong in solving this?

Thanks!
• Nov 19th 2012, 04:46 PM
MarkFL
Re: Rational Expression With Two Variables
We are given to simplify:

$\frac{9r^2-4s^2}{9r+6s}$

Now, factor first, using a difference of squares for the numerator:

$\frac{(3r+2s)(3r-2s)}{3(3r+2s)}$

Cancel or divide out common factors to get:

$\frac{3r-2s}{3}$
• Nov 19th 2012, 04:50 PM
zsf1990
Re: Rational Expression With Two Variables
Wow, I just got done covering factoring too. Thanks so much!