Ok. I gotta do the fraction decomposition of

$\displaystyle \frac{6x^2+1}{x^2(x-1)^3}$.

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My problem is when I get to the part where I figure out what goes into A-E. I'll show the work I have right now below.

$\displaystyle 6x^2+1=A[x(x-3)]^3+B(x-1)^3+C[x^2(x-1)^2]+D[x^2(x-1)]+Ex^2$

$\displaystyle 6x^2+1=A(x^4+3x^3+3x^2-x)+B(x^3 + x^2 + 3x-1)+C(x^4-2x^3+x^2)+D(x^3-x^2)+Ex^2$

$\displaystyle 6x^2+1=(A+C)x^4+(3A+B-2C+D)x^3+(3A+3B+C-D+E)x^2+(-A-B)x+(-B)$

Given the highest power of the numerator is $\displaystyle x^2$. I'm really at a lost what to do from here. I'm not even sure if I'm doing it right. So some help would be greatly appreciated

EDIT: I'm gonna go rework this, something tells me I'm really close to the answer.