Calulus partial fractions

Hello.  I'm struggling with calculus and wondering if any math geniuses/professors/nerds/fellow struggling students can help me out.  For starters, I'm kind of confused about the algebra part of the partial fractions method.  For example, say you have

(3X² + 2x +5)/(x-a₁)²(x-a₂)

Apparantly this converts to:

A/ (x-a₁)² + B/(x-a₁) + C/(x-a₂)



Instead of just:

A/ (x-a₁) + B/(x-a₁) + C/(x-a₂)



Why do I need to square the extra (x-a₁) factor? Needless to say, my textbook is not very clear, and teacher, well... Any help would be greatly appreciated.





That is correct. To say why, I would have to delve into deep, disturbing areas of my brain...

Edited:

Whoops sorry completely wrong math, I saw the thing completely wrong.

Have you seen this? ... http://www4.ncsu.edu/unity/lockers/users/f/felder/public/kenny/papers/partial.html

artfizz: Thanks.  Interesting site. I understand how to solve them though.  I was looking more for an explanation of why the extra factor has to be squared rather than how to solve the resulting sum of partial fractions.