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Can someone tell me where I'm wrong with the taylor series?

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    hi guys

    I want to get taylor series of this function:

    http://www.wolframalpha.com/input/?i...%29+%2C+x0%3D0

    now considering taylor expansion by den. and num. only we have:

    2 x^2-(4 x^4)/3+O(x^6)............ / x^2-(x^4/2)+O(x^6)..........

    as you see, running a simple polynomial division, eliminates all x variables so in the end there'd be only numbers coming out. which shouldn't be the case...can you see where I'm wrong? thanks
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    How does polynomial long division eliminate all the x variables? The coefficients are different, so that's impossible.

    Assuming your Taylor expansions for x\sin 2x and \ln (1+x^2) are correct, what you should do is write it as

    \left( 2x^2 - \dfrac{4}{3} x^4 + O(x^6) \right) \left( x^2 - \dfrac{1}{2}x^4 + O(x^6) \right)^{-1}

    and then use some kind of binomial-ish expansion on the second bracket.
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    that some kind of binomial-ish expansion on the second bracket is what I was asking....

    edit: got the answer!! ok thanks

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