若x/(x-2)^2=A/x-2+B/(x-2)^2(A,B为常数)则A=_B___

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若x/(x-2)^2=A/x-2+B/(x-2)^2(A,B为常数)则A=_____B_______
若x/(x-2)^2=A/x-2+B/(x-2)^2(A,B为常数)则A=_____B_______

若x/(x-2)^2=A/x-2+B/(x-2)^2(A,B为常数)则A=_____B_______
A/x-2+B/(x-2)²
=[A(x-2)+B]/(x-2)²
=[Ax+(B-2A)]/(x-2)²
=x/(x-2)²
所以
Ax+(B-2A)=X
则A=1,B-2A=0
所以
A=1,B=2