# Splitting up a fraction

1. Mar 5, 2012

### 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?

2. Mar 5, 2012

### 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)

3. Mar 6, 2012

### 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?

4. Mar 6, 2012