# Thread: help with partial fractions

1. ## help with partial fractions

Can someone tell me how to put these partial fractions in line?

A/s + B/S^2 + C/S-1 + D/S-2

so I get

1 + 2S = A( ? ) + B( ? ) + C( ? ) + D( ? )

I know 2 and 3 partial fractions by memory so dont know how to figure 4 out

2. I know 2 and 3 partial fractions by memory so dont know how to figure 4 out.
This is why it's better to know the procedure, not memorize some formula. I'm unsure how best to help you without knowing the original problem. Could you please state that?

3. yeah the question is put:

1 + 2S/(S-1)(S-2)(S^2)

into their partial fractions.

4. You need to be more careful with your parentheses. Technically, you wrote 1+((2s)/(S-1))(S-2)(S^2), not, as I suspect you mean, (1+2s)/((S-1)(S-2)(S^2)).)

Ok. I like your initial guess as to how to break down the partial fractions. In order to continue, you need to get a common denominator (which is always going to be equal to the original common denominator, so that's easy to figure out). Just multiply every fraction top and bottom by what's "missing" in that fraction's denominator. Example:

$\displaystyle \dfrac{A}{s}=\dfrac{As(s-1)(s-2)}{s^{2}(s-1)(s-2)}.$

Can you continue from here?

5. not really sure what you have done there, I struggle with maths alot. So what would that look like when you put them in line?

6. All I did there was multiply the fraction on the left by $\displaystyle s(s-1)(s-2)$ top and bottom. I chose that multiplier, because that's what I need in order to get the common denominator.

7. still not really what you mean. Im a final year electrical engineering student and can easily memorise formulas and apply them to problems but dont know how their derived. This is the same as the partial fractions I have only done 2 or 3 partial fractions and have memorised the positions but not sure why their in those positions so thats why I cant do this 4 partial fraction problem. If ya know what I mean.

8. Ok. Let me use an analogy from adding numerical fractions. Let's say you want to perform the following addition:

$\displaystyle \dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{5}+\dfrac{1}{7 }.$

How would you go about it?

9. find the common multiple factor then add the top parts I think.

10. Right. So, turn the crank, and what do you get?

11. not sure at all. I thought the denominator couldnt be put in 1 part and we need to find the 4 top parts so its the question of what from the bottom goes with the top parts.

12. This is not a trick question. Just show me the next step.

13. I get to this point (A+B+C+D)/(S-1)(S-2)(S^2) then cant see what and how many parts from the bottom go to the top. At a guess A would be A(S^2) but thats just guessing.

14. No, no. You're skipping steps, for one thing, and you're not doing what I ask you, for another. See here:

1. In order to solve your problem, you need to understand the procedure of partial fractions thoroughly.
2. It seems to me that your biggest stumbling block with partial fractions (at least right now) is adding up your guesses on the RHS.
3. The basic procedure there is getting common denominators.
4. Therefore, I want to show you how you get common denominators.

Therefore, I want you to focus on the addition problem in post # 8. Show me the next step. How do you get the common denominators?

15. you find the common denominator and add the top parts

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