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为了求A,变成
3/(x^2-x+1)=A+(Bx+C)(x+1)/(x^2-x+1)
令x=-1得到A=1
(重点)为了求B和C,变成
3/(x+1)=A(x^2-x+1)+(Bx+C)
令x^2-x+1=0,于是x^2=x-1
3/(x+1)=Bx+C
3=(Bx+C)(x+1)=Bx^2+(B+C)x+C=(2B+C)x+(-B+C)
因此2B+C=0,-B+C=3
B=-1,C=2