若3x+7/(x-1)(x-2)=A/x-1+B/x-2 则A= B=

来源:学生作业学帮网 编辑:学帮网 时间:2024/04/29 11:07:04

若3x+7/(x-1)(x-2)=A/x-1+B/x-2 则A= B=

3x+7/(x-1)(x-2)=A/x-1+B/x-2
3x+7/(x-1)(x-2)=A(x-2)/(x-1)(x-2)+B(x-1)/(x-1)(x-2)
3x+7/(x-1)(x-2)=[A(x-2)+B(x-1)]/(x-1)(x-2)
3x+7=Ax-2A+Bx-B
3x+7=(A+B)x-(2A+B)
A+B=3,2A+B=-7
A=-10,B=13

A=-10, B=13