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Partial Fractions Question

I'm working on a partial fractions question:

Express f(x) in partial fraction form, where:

f(x) = (6+2x+2x^2-2x^3)/[(x+1)(x-1)^2(x^2+1)].

I have split the fraction into A/(x+1) + B/(x-1) + C/(x-1)^2 + (Dx+E)/(x^2+1)

and then written it as 6+2x+2x^2-2x^3 = A(x-1)^2(x^2+1)+B(x+1)(x^2+1)(x-1)+C(x+1)(x^2+1)+(Dx+E)(x-1)(x-1)^2

I think that you have to compare letters multiplied with the x's on the right with the coefficients of x on the left but I'm not sure how to begin working this through.
Any help would be appreciated. Thanks.

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