已知60/(x+1)(x-2)(x+3) = A/x+1 + B/x-2 + C/x+3 且A,B,C为常数,求A+B+C=?_数学解答

已知60/(x+1)(x-2)(x+3) = A/x+1 + B/x-2 + C/x+3 且A,B,C为常数,求A+B+C=?

人气：112 ℃　时间：2020-03-21 15:36:01

解答

A/x+1 + B/x-2 + C/x+3=[A(x-2)(x+3)+B(x+1)(x+3)+C(x+1)(x-2)]/[(x+1)(x-2)(x+3)]=60/(x+1)(x-2)(x+3) 因此A(x-2)(x+3)+B(x+1)(x+3)+C(x+1)(x-2)=60（恒等于）A(x^2+x-6)+B(x^2+4x+3)+C(x^2-x-2)=60(A+B+C)x^2+(A+4...