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1. Express f(x) = 2 / (2 - 3x + x^2) in partial fractions, ad hence obtain f(x) as a series of ascending powers of x, giving the first four non-zero terms of this expansion. State the set of values of x for which this expansion is valid.

so i have factorised the quadratic and got (2 - x)(1 - x)
but i am a bit confused as to how the partial fraction answer is
(2 / (2 - x)) - (2 / (1 - x))

why is it minus the other fraction? all the other examples in my book are plus. is ita rule when the factorised form has got a number minus x on both of the factor brackets.

and i dont quite understand what to do for the expansion. do i use the binomial expansion method (c4 one) or something else

2. anyone?
3. (Original post by goerigi)
Express f(x) = 2 / (2 - 3x + x^2) in partial fractions, ad hence obtain f(x) as a series of ascending powers of x, giving the first four non-zero terms of this expansion. State the set of values of x for which this expansion is valid.

so i have factorised the quadratic and got (2 - x)(1 - x)
but i am a bit confused as to how the partial fraction answer is
(2 / (2 - x)) - (2 / (1 - x))

why is it minus the other fraction? all the other examples in my book are plus. is ita rule when the factorised form has got a number minus x on both of the factor brackets.

and i dont quite understand what to do for the expansion. do i use the binomial expansion method (c4 one) or something else

If you work through the partial fractions, you'll get that the numerator of one is +2, and the other is -2. Putting those values in gives you the result. It's exactly the same as writing:

(2 / (2 - x)) + (-2 / (1 - x))

You're correct in thinking that you just use the binomial expansion for the second part.
4. (Original post by EEngWillow)
If you work through the partial fractions, you'll get that the numerator of one is +2, and the other is -2. Putting those values in gives you the result. It's exactly the same as writing:

(2 / (2 - x)) + (-2 / (1 - x))

You're correct in thinking that you just use the binomial expansion for the second part.
ok thanks

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