Would very much appreciate verification of solution to partial fraction decomposition question.

Find the partial fraction decomposition of x^4/(x-1)^3

Since degree of numerator is greater than denominator ... long division gives

3x^3-3x^2+x. Since degrees are same, another long division gives:

6x^2 -8x +3.

With A/(x-1) + B/(x-1)^2 + C/(x-1)^3

My solution is: A=6, B=4 and C=1

But my "check" does not compute.

Appreciate any help or redirection.

Doris