Partial Fraction Decomposition: Rules for Multiple Fractions

In summary, the conversation is about partial fractions and how to split a fraction into multiple parts. The formula for f/(p.q.r) is discussed and it is explained that if f/(p.q.r) = A/p + B/q + C/r, then multiplying both sides by pqr will result in f = A.qr + B.pr + C.pq. The question is raised about what happens when the fraction is split into three parts and what constants get multiplied by which denominator. The speaker suggests scanning the book for clarification and the other person agrees to take a picture for them.
  • #1
1MileCrash
1,342
41
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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  • #2
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
 
  • #3
So, multiply by the other two for all three? I had hoped that was the case. Hard to tell what my book did..
 
  • #4
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.
 
  • #5
Ill take a picture when I get out of class, thanks!
 

FAQ: Partial Fraction Decomposition: Rules for Multiple Fractions

What are partial fraction rules?

Partial fraction rules are mathematical techniques used to break down a complex rational expression into simpler partial fractions. These rules are used to solve integrals and other mathematical problems.

Why are partial fraction rules important?

Partial fraction rules are important because they allow us to solve complicated mathematical problems in a more efficient and organized manner. They also help us to better understand the behavior of rational functions.

What are the basic steps for using partial fraction rules?

The basic steps for using partial fraction rules are as follows:

  1. Factor the denominator of the rational expression.
  2. Write the expression as a sum of partial fractions with undetermined coefficients.
  3. Find the values of the coefficients by equating the original expression to the partial fraction expression.
  4. Integrate the individual partial fractions.

Can partial fraction rules be used for any rational expression?

No, partial fraction rules can only be used for proper rational expressions, where the degree of the numerator is less than the degree of the denominator.

Are there any limitations to using partial fraction rules?

Yes, there are a few limitations to using partial fraction rules. For example, the denominator of the rational expression must be factorable into linear and/or quadratic factors. In addition, the coefficients of the partial fractions must be distinct.

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