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    Express  \dfrac{3-x}{(2+x)(1-2x)} in terms of partial fractions and hence, or otherwise, obtain the first three terms in the expansion of this expression in ascending powers of x. State the values of x for which the expansion is valid.

     3-x = A(2+x) + B(1-2x)

    x = -2

     5 = B(1-2\times-2)

     B = 5

    x = 1/2

     \frac{5}{2} = A(\frac{5}{2})

     A = 1

    Therefore

     \dfrac{3-x}{(2+x)(1-2x)} = \dfrac{1}{2+x} + \dfrac{1}{1-2x}


    I have no clue what the rest of the question wants. Can somebody put me in the right direction?
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    Expand your two new fractions for the first 3 terms (x^0 ,x^1 and x^2) and then add the coefficients.

    Have you done binomial expansion but not for integers yet? (Can't remember the proper name )
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    It might help you to write \dfrac{1}{3-x} as \dfrac{1}{3} \times \dfrac{1}{1-\frac{1}{3}x}.

    Consider the formula for the sum to infinity of the geometric series 1+ax+(ax)^2 + (ax)^3 + (ax)^4 + \cdots (from C2). How does this relate to your partial fractions? In particular, how might you write the partial fractions in ascending powers of x

    Equivalently, if you've done the Binomial theorem, write your partial fractions as (3-x)^{-1} + (1-2x)^{-1} and expand them both using the formula for (a+b)^n.
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    (Original post by turn and fall)
    Express  \dfrac{3-x}{(2+x)(1-2x)} in terms of partial fractions and hence, or otherwise, obtain the first three terms in the expansion of this expression in ascending powers of x. State the values of x for which the expansion is valid.

    ...


    I have no clue what the rest of the question wants. Can somebody put me in the right direction?
    As mentioned above you need to write down your
     \dfrac{3-x}{(2+x)(1-2x)} = \dfrac{1}{3-x} + \dfrac{1}{1-2x}
    as:
      (3-x)^-^1 + (1-2x)^-^1

    assuming you know the binomial expantion manipulate to get your function in the form
      a^-^1(1- x/a)^-^1 + (1-2x)^-^1

    Expand each term....and sum the corresponding terms for  x^0,  x^1,  x^2 etc.



    EDit: damit! someone beat me to it...
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    got it - cheers guys
 
 
 
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