Math Is Fun Forum

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."

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.

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.