(6x^2+16x+18)/(x+1)(x+2)(x+3)将下列各题分解为部分分式

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(6x^2+16x+18)/(x+1)(x+2)(x+3)将下列各题分解为部分分式

(6x^2+16x+18)/(x+1)(x+2)(x+3)将下列各题分解为部分分式
(6x^2+16x+18)/(x+1)(x+2)(x+3)
将下列各题分解为部分分式

(6x^2+16x+18)/(x+1)(x+2)(x+3)将下列各题分解为部分分式
分解部分分式,一般采用待定系数法.
设(6x^2+16x+18)/(x+1)(x+2)(x+3)=a/(x+1)+b/(x+2)+c/(x+3)
=[(a+b+c)x^2+(5a+4b+3c)x+(6a+3b+2c)]/(x+1)(x+2)(x+3)
因此有:a+b+c=6,5a+4b+3c=16,6a+3b+2c=18
解这个三元一次方程组得:a=4,b=-10,c=12
所以(6x^2+16x+18)/(x+1)(x+2)(x+3)=4/(x+1)-10/(x+2)+12/(x+3)

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