已知分式方程(x+3)/(x-2)²＝A/(x-2)+B/(x-2)²,求A,B的值

已知分式方程(x+3)/(x-2)²＝A/(x-2)+B/(x-2)²,求A,B的值
已知分式方程(x+3)/(x-2)²＝A/(x-2)+B/(x-2)²,求A,B的值

已知分式方程(x+3)/(x-2)²＝A/(x-2)+B/(x-2)²,求A,B的值
两边乘以(x-2)²得
x+3=A(x-2)+B
=AX+(B-2A)
∴A=1
b-2A=3
∴A=1
B=5