右边通分
=A(x-2)/(x-1)(x-2)+B(x-1)/(x-1)(x-2)
=[A(x-2)+B(x-1)]/(x-1)(x-2)
=(Ax-2A+Bx-B)/(x-1)(x-2)
=[(A+B)x+(-2A-B)]/(x-1)(x-2)
=(3x+7)/(x-1)(x-2)
所以(A+B)x+(-2A-B)=3x+7
所以x系数和常数项分别相等
所以A+B=3
-2A-B=7
相加
-A=10
A=-10
B=3-A=13