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#### xxbassplayerxx

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Hey guys. I have an exam tomorrow and I was reading through the book doing the examples. Since partial fractions is algebra (maybe early calculus), the book's authors don't explain how to do it whenever they use it. I can normally do them, but I seem to have run into a particularly difficult example.

To get from the second step to the third step, it says they used partial fractions. If anyone could fill out the step between the two I would be extremely grateful.

Here's the problem:

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split the fraction into As + B and Cs + D each over one of the factored polynomials in the denominator and equate to complete fraction like so:

3s/((s^2 + 4)(s^2 +1)) = (As + B)/(s^2 + 4) + (Cs + D)/(s^2 +1)

multiply both sides by the denominator of the complete fraction:

3s = (As + B)(s^2 + 1) + (Cs + D)(s^2 + 4)

Then solve for A, B, C and D by grouping common degrees of s: (all the s together, all the s^2 together and all the constants together. If there is none on one side put a zero)

0 = As^3 + Cs^3
0 = Bs^2 + Ds^2
3s = 4As + Cs
0 = B + 4D

4 equations and 4 variables so you can solve for A,B,C,and D. Then you can stick the values back into the first equation. (Turns out A = -1, C = 1, B = 0 and D = 0)

Hope this helps
My ODE test is next week and this was a good little review for me

• xxbassplayerxx

#### xxbassplayerxx

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Ahah! I forgot you could do the grouping thing! Thank you so much. Very helpful.

Now how to go about giving more than one rep...

#### Ryanb213

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Quote:
 Originally Posted by xxbassplayerxx Ahah! I forgot you could do the grouping thing! Thank you so much. Very helpful. Now how to go about giving more than one rep...