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(4x-4)/(x^4 -2x^3 +4x^2 -6x +3)

which factors to

(4x-4)/(x^2+3)(x-1)^2

now I have the answer here. but I don't know the rules for decomposing this fraction. can someone go over them for me

this decomposes to A + B/(x-1)^2 + Cx+D/(x^2+3)

i don't understand this step, why is the A value by itself, and what is the determining factor that you have 2 terms in the numerator. I though it had something to do with the degree of the denominator. but then why is it B/(x-1)^2 for the one but Cx+D/(x^2+3) for the other. both are x^2 terms.

hope i've explained myself well enough,

thanks