What is the result of performing partial fraction decomposition on the rational function x^2-6/(x-1)^2(2x+3)?

As it stands you can't because you don't have a polynomial denominator. However if you had 1/(x^3 + 2x^2 + 2x) than yoou could do it like this: 1/(x^3 + 2x^2 + 2x) =1/(x(x^2 + 2x^2 + 2)) =1/(x(x + 1)^2) = A/x + B/(x+1) + C/(x+1)^2 where 1 = A(x+1)^2 + Bx(x+1) + Cx setting x = 0 1 = A setting x=-1 1 = -C :. C=-1 comparing coefficients in x^2 0 = A + B :.

B = -1 1/(x^3 + 2x^2 + 2x) = 1/x - 1/(x+1) - 1/(x+1)^2.

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