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#1 2006-10-06 10:18:31

yonski
Member
Registered: 2005-12-14
Posts: 67

Partial Fractions

Hi there,
what's the best way to convert improper fractions to partial fractions? I'm using this sort of method at the moment...

(4x^3 + 10x + 4) / x(2x + 1)  =  Ax + B + C/x  + D/(2x + 1)

and then working out A, B, C, D etc by putting in values for x, or equating the coefficients. This usually works fine, until I came across this one

(x^3 + 1) / (x^2 + 1)

and suddenly my method seems to collapse. Is this a good method to use or is there a better one?

Thanks.


Student: "What's a corollary?"
Lecturer: "What's a corollary? It's like when a theorem has a child. And names it corollary."

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#2 2006-10-06 10:35:30

polylog
Member
Registered: 2006-09-28
Posts: 162

Re: Partial Fractions

I would suggest carrying out polynomial long division, and then what you obtain from that would be a proper fraction plus another term.

Then the proper fraction has known cases of partial fraction decomposition, which is all straighforward.

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#3 2006-10-06 12:20:44

polylog
Member
Registered: 2006-09-28
Posts: 162

Re: Partial Fractions

For your example, using polynomial long division:

This can be written as:

And I don't think it can be made any simpler.

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