Question

已知(x-3)/(x^2-3x+2)=A/(x-1)-B/(x-2),求A,B

Answer 1

通分(x-3)/(x^2-3x+2)=A/(x-1)-B/(x-2)=(（x-2）A-（x-1)B)/(x^2-3x+2)=
所以x-3=（x-2）A-（x-1)B=（A-B）x-2A+B
即A-B=1
3=2A-B
所以A=2 B=1

Answer 2

(x-3)/(x^2-3x+2)=A/(x-1)-B(x-2)
(x-3)/(x-1)(x-2)=[A(x-2)-B(x-1)]/(x-1)(x-2)
x-3=A(x-2)-B(x-1)
x-3=Ax-2A-Bx+B
x-3=(A-B)x-(2A-B)
所以A-B=1，2A-B=3
得A=2，B=1