# quick question with simplifying rational expressions

• Jul 6th 2008, 05:06 PM
Hypertension
quick question with simplifying rational expressions
I just need some confirmation to whether or not these are right,

can I simplify $\displaystyle -\frac{3x^2}{2x}$ into $\displaystyle \frac{3x}{2}$?

can $\displaystyle \frac{x+3}{x+6}$ be simplified to $\displaystyle \frac1{2}$?
• Jul 6th 2008, 06:23 PM
Jonboy
on the first you're correct. and let me tell you why.

you have: $\displaystyle \frac{ - 3x^2}{2x}$

Pull out the x on top and bottom: $\displaystyle \frac{ x(-3x)}{x(2)}$

this is the same as: $\displaystyle \frac{x}{x}\cdot \frac{-3x}{2}$

$\displaystyle \frac{x}{x}$ is one. anything divided by itself is one (except zero).

So you're left with: $\displaystyle 1\cdot\frac{-3x}{2} = \frac{-3x}{2}$

you can just cancel the x's: $\displaystyle \frac{ \not x(-3x)}{\not x(2)}$

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On the second problem, you're wrong.

There's nothing you can factor out on the top and bottom.

but say you had: $\displaystyle \frac{4x + 8}{2x + 6}$

now you can pull out factors: $\displaystyle \frac{2(2x + 4)}{2(x + 3)} = \frac{ \not 2 (2x + 4)}{ \not 2 (x + 3)}$

$\displaystyle = \frac{2x + 4}{x + 3}$
• Jul 6th 2008, 06:34 PM
Hypertension
Thank you