已知实数A,B满足x+3/(x-2)²=A/x-2+B/（x-2）².求AB值

已知实数A,B满足x+3/(x-2)²=A/x-2+B/（x-2）².求AB值
已知实数A,B满足x+3/(x-2)²=A/x-2+B/（x-2）².求AB值

已知实数A,B满足x+3/(x-2)²=A/x-2+B/（x-2）².求AB值
右边通分
=[A(x-2)+B]/(x-2)²
=[Ax+(B-2A)]/(x-2)²
=(x+3)/(x-2)²
则Ax+(B-2A)=x+3
所以A=1
B-2A=3
所以
A=1
B=3+2A=5