# Stupid question about partial fraction decomposition:

##### Diamond Member
I forgot my calc book in my locker and all my friends are at school (I'm sick today so I couldn't make it).

Anyway I'm trying to figure out how to decompose: 2/[x^3 * (x^2+9)]

Thanks. I forgot what the rules where, and when to use Ax+B and such.

Thanks again.

bump!

##### Member
see this example, if it all it helps

Example

#### Kyteland

##### Diamond Member
That equation would decompose in to this:

A/x + B/x^2 + C/x^3 + (D*x+E)/(x^2+9)

You should be able to solve the rest from that.

##### Diamond Member
Originally posted by: Kyteland
That equation would decompose in to this:

A/x + B/x^2 + C/x^3 + (D*x+E)/(x^2+9)

You should be able to solve the rest from that.
Thanks. I can solve it from here.

But my question is, why does it decompose to that?

#### TuxDave

##### Lifer
In partial fraction decomposition, the denominators need to be factors of the overall denominator. So let's take your example of:

x^3*(x^2+9) as the denominator

You can technically decompose it into ones with X^3 and X^2+9 as denonators, but you can further decompose the X^3 into terms of X and X^2. So to get all the possible combinations you need denominators of.

X, X^2, X^3, X^2+9

As for the numerator, it could be any polynomial with a smaller order.

##### Diamond Member
Originally posted by: TuxDave
In partial fraction decomposition, the denominators need to be factors of the overall denominator. So let's take your example of:

x^3*(x^2+9) as the denominator

You can technically decompose it into ones with X^3 and X^2+9 as denonators, but you can further decompose the X^3 into terms of X and X^2. So to get all the possible combinations you need denominators of.

X, X^2, X^3, X^2+9

As for the numerator, it could be any polynomial with a smaller order.
Ok makes sense. However, if in the numerator polynomial has to be off smaller order, then shouldn't the numerator of x^3 be Cx^2?

I mean to say, why does only the numerator of x^2+9 have to be Dx + E.

#### TuxDave

##### Lifer
Originally posted by: TuxDave
In partial fraction decomposition, the denominators need to be factors of the overall denominator. So let's take your example of:

x^3*(x^2+9) as the denominator

You can technically decompose it into ones with X^3 and X^2+9 as denonators, but you can further decompose the X^3 into terms of X and X^2. So to get all the possible combinations you need denominators of.

X, X^2, X^3, X^2+9

As for the numerator, it could be any polynomial with a smaller order.
eh... get back to you on it...
I mean to say, why does only the numerator of x^2+9 have to be Dx + E.
lol.. my brain is retarded. Ok, so for x^2+9, it has to be dx+e because that is a polynomial of a lesser order. But x,x^2,and x^3 are all derived from the same factor, x^3. x^3 used to be ax^2+bx+c/x^3 if we didn't break it down. But I guess it's hard to show but you can break ax^2+bx+c/x^3 = d/x+e/x^2+f/x^3... ok, I suck, who's next?