# simplify rational expression

• Mar 21st 2010, 07:19 PM
simplify rational expression
Please help, I have a test tomorrow. Simplify: $\displaystyle 2x^3 + x^2 / 6x^3 - 3x^2 - 3x$ The "/" means divide them...

Could you please show the steps? The answer is supposed to be $\displaystyle x/3(x + 1)$ but I have no idea how to get that.
• Mar 21st 2010, 07:35 PM
Stroodle
$\displaystyle \frac{2x^3+x^2}{6x^3-3x^2-3x}=\frac{x^2(2x+1)}{(2x+1)(3x^2-3x)}$

Can you take it from there?

The answer you gave is wrong by the way :)
• Mar 21st 2010, 07:46 PM
Quote:

Originally Posted by Stroodle
$\displaystyle \frac{2x^3+x^2}{6x^3-3x^2-3x}=\frac{x^2(2x+1)}{(2x+1)(3x^2-3x)}$

Can you take it from there?

The answer you gave is wrong by the way :)

Um, so would it become $\displaystyle \frac{x^2}{3x^2 - 3x}$? Then... how would you factor the denominator?

Btw you are a LIFESAVER thank you so much!
• Mar 21st 2010, 07:50 PM
Stroodle
No probs :)

$\displaystyle \frac{x^2}{3x^2-3x}=\frac{x\times x}{3x(x-1)}=\frac{x}{3(x-1)}$