题目

如果1+x/3x^2-2x-1=A/3x+1+B/x-1,求A,B的值

提问时间：2021-02-22

答案

1+x/3x^2-2x-1=A/3x+1+B/x-1,
(1+x)/(3x^2-2x-1)=A/(3x+1)+B/(x-1),
(x+1)/[(3x+1)(x-1)]=A/(3x+1)+B/(x-1),
其中：A/(3x+1)+B/(x-1)
=[A(x-1)+B(3x+1)]/[(3x+1)(x-1)]
=[Ax+3Bx+B-A]/[(3x+1)(x-1)]
=[x(A+3B)+(B-A)]/[(3x+1)(x-1)]
(x+1)/[(3x+1)(x-1)]=[x(A+3B)+(B_A)]/[(3x+1)(x-1)]
(x+1)=[x(A+3B)+(B-A)]
x=x(A+3B)-----A+3B=1
A+3B=1
B-A=1
解方程组：4B=2,B=1/2.A=B-1=1/2-1=-1/2
A= - 1/2
B=1/2