Simplifying Rational Expressions

Simplify the expression. State any excluded values.

Question

Simplifying Rational Expressions

Simplify the expression. State any excluded values.

anonymous · Answer

$$ \frac{ 2x ^{2} + 6? }{ 10x ^{3} }$$

e.mccormick · Answer

Well, you can factor out a 2 pretty easy, but it does not look to be friendly to much more than that.  The important part is that whole, "State any excluded values."  That means you need to say when it would be invalid as an equation.  Like all fractions, what makes it invalid is if 0 is in the divisor.

anonymous · Answer

I still dont understand.

e.mccormick · Answer

OK.  Which part?  The "State any excluded values?"

anonymous · Answer

The whole thing. Like I read the book but I still don't understand it and I have to do my whole chapter 11 math book in like 48 hours because I am just so excited to be done with Algebra 1 for the year! (:

e.mccormick · Answer

Ah, and I see there is a ?  in there.  Was that supposed to be there?

anonymous · Answer

no.

anonymous · Answer

I meant x!

e.mccormick · Answer

OK.

e.mccormick · Answer

You get the simplify part?  Doing this sort of thing with it?
$$\frac{ 2x ^{2} + 6x }{ 10x ^{3} }\implies \frac{ 2x(x + 3) }{ 2x(5x ^{2}) } \implies \frac{ x + 3 }{ 5x ^{2} }$$

anonymous · Answer

no i dont get any part of it...

e.mccormick · Answer

What I did there was notice that every term had an x in it and every term was even.  That told me that I could factor out the 2x.

Simplification is really the same in algebra as it is with regular fractions.  For example:
$$\frac{3}{9}=\frac{1}{3}$$You just look for things you can cancel like that.

anonymous · Answer

okay

e.mccormick · Answer

$$\frac{ 2x ^{2} + 6x }{ 10x ^{3} }$$ Makes it a bit harder to see, but the idea is the same.  Look for factors, things that multiply, that can come out.
I know I am beating this to death, but I just want to saay it a few ways and times to give you the best chance of getting it.

anonymous · Answer

so howd you get (2 + x) (x + 3)? You simplified 6?

e.mccormick · Answer

I didn't get $2+x$.  I got 2x.
$$\frac{ 2x ^{2} + 6x }{ 10x ^{3} }\implies \frac{ 2x(x + 3) }{ 2x(5(x ^{2}) }$$
Factoring out is, well, Un-Multiplying.  

$5\times 3=15$ and by the same token $15=5\times 3$  Well, $2x ^{2} + 6x =  2x(x + 3) $ works the same way.

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