分式.(19 15:44:10)
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分式.(19 15:44:10)
若X2+2/X(X+1)(X+2)=A/X+B/X+1+C/X+2,试求A、B、C的值.
若X2+2/X(X+1)(X+2)=A/X+B/X+1+C/X+2,试求A、B、C的值.
![分式.(19 15:44:10)](/uploads/image/z/8754664-40-4.jpg?t=%E5%88%86%E5%BC%8F.%2819+15%3A44%3A10%29)
题目(x²+2)/(x(x+1)(x-1))=A/x+B/(x+1)+C/(x+2)
A/x+B/(x+1)+C/(x+2)通分,得:[(A+B+C)x²+(3A+2B+C)x+2A]/[x(x+1)(x-1)]
对应系数相等,得:A+B+C=1,3A+2B+C=0,2A=2
解出A=1,B=-3,C=3
A/x+B/(x+1)+C/(x+2)通分,得:[(A+B+C)x²+(3A+2B+C)x+2A]/[x(x+1)(x-1)]
对应系数相等,得:A+B+C=1,3A+2B+C=0,2A=2
解出A=1,B=-3,C=3