已知(2x-3)/(x-1)(x+2)=A/(x-1) + B/(x=2) ,求A,B的值

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已知(2x-3)/(x-1)(x+2)=A/(x-1) + B/(x=2) ,求A,B的值
已知(2x-3)/(x-1)(x+2)=A/(x-1) + B/(x=2) ,求A,B的值

已知(2x-3)/(x-1)(x+2)=A/(x-1) + B/(x=2) ,求A,B的值
2X-3/(X-1)(X+2)=A/X-1 + B/X+2
[2x-3]/(x-1)(x+2)=[A(x+2)+B(x-1)]/(x-1)(x+2)
(2x-3)/(x-1)(x+2)=[(A+B)x+(2A-B)]/(x-1)(x+2)
所以:
A+B=2
2A-B=-3
A=-1/3
B=7/3

(2x-3)/(x-1)(x+2)=A/(x-1) + B/(x+2)
=(A(x+2)+B(x-1))/(x-1)(x+2)
=((a+b)x+2a-b))/(x-1)(x+2)
所以A+B=2,2A-B=-3
A=-1/3,B=7/3