Decompose x,squre-10x-8/(x-1)squre (x,squre-x+1)into partial fraction

(x^2-10x-8) / (x-1)^2 (x^2-x+1) = A/(x-1) + B/(x-1)^2 + (Cx+D)/(x^2 - x + 1)

placing the right side over a common denominator, you get
x^2-10x-8 = A(x-1)(x^2-x+1) + B(x^2-x+1) + (Cx+D)(x-1)^2
x^2-10x-8 = (A+C)x^3 + (-2A+B-2C+D)x^2 + (-2A-B+C+2D)x + (-A+B+D)
equating coefficients, you have
A+C = 0
-2A+B-2C+D = 1
-2A-B+C+2D = -10
-A+B+D = -8
solve all that, and you have
(x^2-10x-8) / (x-1)^2 (x^2-x+1) = 9/(x-1) - 17/(x-1)^2 - 9(x-2)/(x^2-x+1)