McClaurin Series: f(x) = 1/(3x /\ 2 + 1) - 1/(x + 3)

[PlantPage55]

Hi everybody - first time asking a quesion...

I've got a pretty tough McClaurin Series problem that I need some help with:

What is the Convergence Radius of the following?

. . . . .\(\displaystyle \large{f(x)\, =\,\frac{1}{3x^2\,+\,1} \,-\,\frac{1}{x\,+\,3}}\)

Either I'm getting caught up in some complication - or there is a really easy way of doing it that I can't remember. Thanks Everyone!

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* Post edited for clarity -- stapel *

 

[tkhunny]

Have you tried examining the expansions separately?

\(\displaystyle \L\,g(x) = \frac{1}{x+3}\)

and

\(\displaystyle \L\,h(x) = \frac{1}{3*x^{2}+1}\)