(x2+x-3)/(x-1)(x-2)(x-3)=A/(x-1)+B/(x-2)+C/(x-3).求AB的值

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(x2+x-3)/(x-1)(x-2)(x-3)=A/(x-1)+B/(x-2)+C/(x-3).求AB的值(x2+x-3)/(x-1)(x-2)(x-3)=A/(x-1)+B/(x-2)+C/(x-

(x2+x-3)/(x-1)(x-2)(x-3)=A/(x-1)+B/(x-2)+C/(x-3).求AB的值
(x2+x-3)/(x-1)(x-2)(x-3)=A/(x-1)+B/(x-2)+C/(x-3).求AB的值

(x2+x-3)/(x-1)(x-2)(x-3)=A/(x-1)+B/(x-2)+C/(x-3).求AB的值
两边同乘以(x-1)(x-2)(x-3),得 x2+x-3=A(x-2)(x-3)+B(x-1)(x-3)+C(x-1)(x-2), 所以x2+x-3=Ax2-5Ax+6A+Bx2-4Bx+3B+Cx2-3Cx+2C, 所以x2+x-3=(A+B+C)x2-(5A+4B+3C)x+(6A+3B+2C), 所以A+B+C=1,5A+4B+3C=-1,6A+3B+2C=-3, 解得A=-0.5,B=-3,C=4.5, 所以AB=1.5. 另 两边同乘以(x-1)(x-2)(x-3),得 x2+x-3=A(x-2)(x-3)+B(x-1)(x-3)+C(x-1)(x-2), 所以x2+x-3=Ax2-5Ax+6A+Bx2-4Bx+3B+Cx2-3Cx+2C, 分别取x=1,x=2,x=3,可先后求得A=-0.5,B=-3,C=4.5 所以AB=1.5.