Why doesn't partial fractions work in this case?

[aaaa202]

I want to split the fraction:

2a/((a+1)(a²+4))

I have tried using partial fractions, but came to something that was nonsense, and my question is why that is. Why doesn't partial fractions work in this case, from a mathematical point of view, and is it still possible to split up the fraction?

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Chances are of course that I just used partial fractions the wrong way, so here is how I did:

2a/((a+1)(a²+4)) = C/(a+1) + D/(a²+4)

we have that:

C(a²+4) + D(a+1) = 2a

Which gives us the equations:

Ca² = 0
4C + D = 0
Da = 2a

which clearly contradict each other. What is wrong in my approach?

 

[Dick]

You have a quadratic factor, so your template for partial fractions is wrong. You should start from 2a/((a+1)(a^2+4)) = C/(a+1) + (D+Ea)/(a^2+4)

 

[aaaa202]

Sorry, I never really learned about partial fractions, so could you briefly explain why you (as it appears to be) need a polynomial of one degree lower than the denominator's in the numerator?

 

[Mark44]

http://en.wikipedia.org/wiki/Partial_fraction
You can probably skip down to the section titled Procedure.