# Thread: quick question with simplifying rational expressions

1. ## quick question with simplifying rational expressions

I just need some confirmation to whether or not these are right,

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

can $\frac{x+3}{x+6}$ be simplified to $\frac1{2}$?

2. on the first you're correct. and let me tell you why.

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

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

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

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

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

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

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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: $\frac{4x + 8}{2x + 6}$

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

$= \frac{2x + 4}{x + 3}$

3. Thank you