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C4 ~ Partial Fractions, help please! watch

1. Ok, so have the following partial fraction:

X^2 + X + 1
(X-1)(X+1)(X^2 -1)

which is
A/(X+1) + B/(X-1) + (Cx + D)/(X^2 +1)

By putting x=1 and x=-1 in, can work out B=3/4 and A=-1/4, but then where do you go? Am I on the right tracks?

Any help would be much appreciated!
2. You are on the right tracks. For the next bit you need to compare co-efficients.

You know that:

x^2 + x + 1 = A(x-1)(x^2+1) + B(x+1)(x^2+1) + (Cx+D)(x+1)(x-1)

You already know what A and B are. You know that he coefficient of x^2 on the right-hand side must be 1 and the coefficient of x on the r.h.s. must be 1 and the constant on the r.h.s. must be 1. So now you just need to work out what values of C and D will make this so.

EDIT - And, of course, the 'co-efficient' of x^3 must be zero.
3. Alternatively, you could try putting in another number, chosen at semi-random. Good ones to try are 1, 0, -1, and possibly 2, if none of the others are any use.

x2 + x + 1 = A/(x+1) + B/(x-1) + (Cx + D)/(x2+1)

Let x = 0,

1 = A - B + C + D
1 = -1/4 - 3/4 + C + D
1 = -1 + C + D
2 = C + D

In this case, because you've got two variables, you need to find yet another equation and solve them simultaneously. It is at this point that you want to give up hope and go with comparing coefficients instead :P. Using an arbitary substitution does help sometimes though.
4. Thanks guys!!!

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Updated: February 23, 2006
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