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    Can some explain to me how to do this up to and including the x cubed term? I can do 1/(2+x) but not sure what to do with the x on top. I tried making it two fractions but got some x^6 terms which weren't in the answer books.

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    1+x = (2+x) - 1

    Can you see how this helps you?
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    Cant you just do (1+x)(2+x)^-1 - do the binomial expansion of the second part and then times all the terms by (1+x) or am i missing something somewhere???
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    Do it as (1+x)(2+x)^-1 - when expanding you you'll get terms of higher order than what you expanded (2+x)^-1 to, ignore these.
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    =(1+x)(2+x)^-1
    = (1+x)2^-1(1+ x/2)^-1
    =0.5(1+x)[ 1 + (-1)(x/2) + ((-1)(-2)/2!)(x/2)^2 +....]
    = (0.5 + x/2) [ 1 - 0.5x + 0.25x^2 +...]
    = do the rest yourself
 
 
 
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Updated: February 7, 2010

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