Partial Fraction Decomposition: Rules for Multiple Fractions

1MileCrash
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I hope its not a problem if I don't have an actual problem. I have a question about partial fractions.

When I spilt it into two, the numerator of the original is equal to unknown constant A times secondimerator, plus unknown constant b times first denominator.

What if it is spilt into three fractions? What constant gets multiplied by what denominator?
 
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If f/(p.q.r) = A/p + B/q + C/r

then multip both sides by pqr to get

f = A.qr + B.pr + C.pq
 
So, multiply by the other two for all three? I had hoped that was the case. Hard to tell what my book did..
 
1MileCrash said:
So, multiply by the other two for all three? I had hoped that was the case. Hard to tell what my book did..
You can scan that part of the book that you do not understand.
 
Ill take a picture when I get out of class, thanks!
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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