I'm simplifying rational expressions and don't know how to do this one.

x^3 + 3x^2 - 2x - 6
over
x^3 + 27

I need the steps on how to do it.
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Last edited by carrotcake at Mar 26, 2009,
Maths question?

Maths thread.

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Quote by Trowzaa
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use long division
wow your asking the pit??!?!?! They'd give you an answer like "tats teh nubmer of tymes i didd uur momm!!!ahahahahahahahahaha". In other words don't ask the pit math stuff lol.
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Quote by carrotcake
I'm simplifying rational expressions and don't know how to do this one.

x^3 + 3x^2 - 2x - 6
over
x^3 + 27

I need the steps on how to do it.

i think first thing you have to do is cancel out the x^3 on the top and bottom because when u have exponents as a fraction, you have to subtract so that cancels out. than u hav to simplify -6 over 27 which gives you -2 over 9. so im pretty sure the answer is:

3x^2 - 2x - 6
over
9
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Quote by carrotcake
I'm simplifying rational expressions and don't know how to do this one.

x^3 + 3x^2 - 2x - 6
over
x^3 + 27

I need the steps on how to do it.

+1 to long division. You'll do this:
x^3 + 3x^2 - 2x - 6
------------------------------------------
x^3 + 0x^2 + 0x + 27

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Quote by Trowzaa
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Quote by salrap10
i think first thing you have to do is cancel out the x^3 on the top and bottom because when u have exponents as a fraction, you have to subtract so that cancels out. than u hav to simplify -6 over 27 which gives you -2 over 9. so im pretty sure the answer is:

3x^2 - 2x - 6
over
9

so wrong.....you can only cancel multiplied terms........try again
x^3 + 3x^2 - 2x - 6
-----------------------
x^3 + 27

Factor each.

(x^2 - 2)
----------------
(x^2 - 3x + 9)

Or something like that, I'm sorta lolies right now, but yeah, do it that way.
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Quote by bassx901
so wrong.....you can only cancel multiplied terms........try again

i thought tht since its x^3 over x^3 you have to subtract and tht gives u x^0 which you cant have so it cancels out
Cross out the two x^3
Then you should be able to simplify the 3x^2 - 2x - 6, though I forget how.

-b +/- sqrt(b^2 - 4ac)
over
2a

Maybe?
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Quote by salrap10
i thought tht since its x^3 over x^3 you have to subtract and tht gives u x^0 which you cant have so it cancels out

You don't. You have essentially this:
(x^3 - stuff)
------------------
(x^3 + 27)

Since those aren't the same, you can't factor anything. And since they're added, as opposed to multiplied, you can't divide things out.

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Quote by bfredder92
wow your asking the pit??!?!?! They'd give you an answer like "tats teh nubmer of tymes i didd uur momm!!!ahahahahahahahahaha". In other words don't ask the pit math stuff lol.

Can't be bothered to help OP, but that post is disgustingly stupid. There's a whole thread dedicated to Math Help and there's physics and chemistry ones too.
Quote by salrap10
i thought tht since its x^3 over x^3 you have to subtract and tht gives u x^0 which you cant have so it cancels out

Still wrong... if it was say (x^3)(9) over (x^3)(3x^2) then you could cancel because they are multiplied.

But long division is what I would use. You would get an answer of one and a fraction I think... hold on and I'll do it.
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the answer is x^2 -2 / x^2 - 3x + 9
Quote by bassx901
the answer is x^2 -2 / x^2 - 3x + 9

That's what I got!
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Quote by bassx901
the answer is x^2 -2 / x^2 - 3x + 9

"simplified"

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Quote by bassx901
the answer is x^2 -2 / x^2 - 3x + 9

How do you get that?

TS: I ended up getting 1 + [(3x^2-2x-33)over(x^3 +27)] after long division.
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Quote by ShaunDiel
Can't be bothered to help OP, but that post is disgustingly stupid. There's a whole thread dedicated to Math Help and there's physics and chemistry ones too.
yea but there's those people who go on the pit to piss people off and be funny so thats what i was expecting lol but i guess not.
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Quote by SteveHouse
"simplified"

Simplified means fully factored, in this sort of math anyways, and you can't factor that down anymore.
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Quote by brandon369852
Simplified means fully factored, in this sort of math anyways, and you can't factor that down anymore.

I know this. It's just always been funny to me.

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Quote by Trowzaa
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Quote by brandon369852
Simplified means fully factored, in this sort of math anyways, and you can't factor that down anymore.

Yeah man I see what you are saying, I don't get the point of attempting to break it down any more considering all long division does is change the form and not really the polynomial itself.
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Quote by ATLBraves2014
How do you get that?

TS: I ended up getting 1 + [(3x^2-2x-33)over(x^3 +27)] after long division.

(x^3 + 3x^2) (- 2x - 6)
-----------------------
x^3 + 27

1) take out an x^2 from the first one
x^2(x + 3)
2) take out a -2 from the second
-2(x + 3)
So on the top you have
(x^2 - 2)(x + 3)
---------------------
3) factor the trinomial
(x + 3)(x^2 - 3x + 9)

so it's (x^2 - 2)(x+3)
-------------------
(x+3)(x^2 - 3x + 9)

The (x+3) cancel out, so

(x^2 - 2)
----------
(x^2 - 3x + 9)

Numerator and denominator are both fully factored.
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