已知x+5/(x+1)(x-3)=(A/x+1)+(B/x-3)求整式A,B值

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/07 04:17:48

已知x+5/(x+1)(x-3)=(A/x+1)+(B/x-3)求整式A,B值
已知x+5/(x+1)(x-3)=(A/x+1)+(B/x-3)
求整式A,B值

已知x+5/(x+1)(x-3)=(A/x+1)+(B/x-3)求整式A,B值
右边通分
=[a(x-3)+b(x+1)]/(x+1)(x-3)
=[(a+b)x+(b-3a)]/(x+1)(x-3)
=(x+5)/(x+1)(x-3)
所以(a+b)x+(b-3a)=x+5
所以
a+b=1
b-3a=5
所以a=-1,b=2