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

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- Nov 6th 2010, 01:20 AMhunterage2000help 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 - Nov 6th 2010, 01:45 AMAckbeetQuote:

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

- Nov 6th 2010, 01:49 AMhunterage2000
yeah the question is put:

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

into their partial fractions. - Nov 6th 2010, 01:57 AMAckbeet
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? - Nov 6th 2010, 02:04 AMhunterage2000
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?

- Nov 6th 2010, 02:14 AMAckbeet
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.

- Nov 6th 2010, 02:28 AMhunterage2000
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.

- Nov 6th 2010, 02:38 AMAckbeet
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? - Nov 6th 2010, 02:43 AMhunterage2000
find the common multiple factor then add the top parts I think.

- Nov 6th 2010, 02:47 AMAckbeet
Right. So, turn the crank, and what do you get?

- Nov 6th 2010, 03:01 AMhunterage2000
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.

- Nov 6th 2010, 03:08 AMAckbeet
This is not a trick question. Just show me the next step.

- Nov 6th 2010, 03:22 AMhunterage2000
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.

- Nov 6th 2010, 03:31 AMAckbeet
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? - Nov 6th 2010, 03:54 AMhunterage2000
you find the common denominator and add the top parts