Verified answer

1/((x-1)(x^2-x+1))=A/(x-1)+(Mx+N)/(x2-x+1)

M-?, N-?, A-?

1/((x-1)(x^2-x+1))=(A(x2-x+1)+(Mx+N)(x-1))/(x2-x+1)

знаменатели равны

приравниваем числители

Ax2 - Ax + A + Mx2 - Mx + Nx - N = 1

x2(A + M) - x(A + M + N) + A - N = 1

Систему получили

A + M = 0

A + M + N = 0

A - N = 1

A + M + N - A - M = 0

N = 0

A = 1

M = -1

1/((x-1)(x^2-x+1))=1/(x-1)-x/(x2-x+1)