Math Is Fun Forum

slasherex

Member

Registered: 2009-10-25

Posts: 3

Partial Fractions

please help
forgot how to work this stuff lol

x^3 - x^2 - 3x +5
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(x^2 - 5x + 6) (x-1)

Last edited by slasherex (2009-10-25 10:54:28)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Partial Fractions

Hi slasherex;

First thing you should do is use synthetic division to get a proper fraction. Since the numerator is greater than the denomimator for all x.

Now you can do a partial fraction decomposition on the second term: The denom. factors into 3 different factors. Your form will be of the type:

You have 3 unknowns to solve for, so you form 3 simultaneous equations: You use 1) to get them.

When x = 4 you have from plugging into 1):

When x = 5 you have from plugging into 1):

When x = 0 you have from plugging into 1):

Solve the 3 equations simultaneously.

a=1 , b = - 3 , c = 7

Last edited by bobbym (2009-10-28 09:57:07)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

slasherex

Member

Registered: 2009-10-25

Posts: 3

Re: Partial Fractions

tnx so much for da help bobbym

dont mean to bother u but im just a bit confused at to parts

1. I can work stuff synthetically but Im not sure how you came up with that answer
    so if u cud expound on dat part a bit that wud be great.

2. Also did u use crammer's rule for the 3 simultaneous equations? Im asking because I      cant  remember working a 3 simultaneous question with fractions.

Tnx again Im gon see if I can work at this as soon as as Im done typing this.

Last edited by slasherex (2009-10-25 13:23:17)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Partial Fractions

Hi slasherex;

To get this:

I expanded out the denominator and used long division. There are probably webpages that will do the division for you.

2) Sorry, Cramer's rule is just for show. I suggest gaussian elimination, successive over relaxation methods or again webpages that will solve simultaneous sets for you. If the fractions are bothering you then just multiply by a common factor.

Here is the most basic idea and you should be familiar with it.

Times both sides by 6 gives you:

Times by 12 gives you:

Times by -6 gives you:

I have cleared the fractions away. Try to solve that set of equations on your own.

Last edited by bobbym (2009-10-28 09:58:10)

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.