X(x+3)分之一+(X+3)(X+6)分之一+(X+6)(X+9)分之一=2x+18分之三快

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X(x+3)分之一+(X+3)(X+6)分之一+(X+6)(X+9)分之一=2x+18分之三快
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X(x+3)分之一+(X+3)(X+6)分之一+(X+6)(X+9)分之一=2x+18分之三快
X(x+3)分之一+(X+3)(X+6)分之一+(X+6)(X+9)分之一=2x+18分之三

X(x+3)分之一+(X+3)(X+6)分之一+(X+6)(X+9)分之一=2x+18分之三快
1/x(x+3)+1/(x+3)(x+6)+1/(x+6)(x+9)=3/2(x+9)
(1/3)×[3/x(x+3)+3/(x+3)(x+6)+3/(x+6)(x+9)]=3/2(x+9)
(1/3)[(1/x-1/(x+3)+1/(x+3)-1/(x+6)+1/(x+6)-1/(x+9)]=3/2(x+9)
(1/3)[1/x-1/(x+9)]=3/2(x+9)
1/3x=3/2(x+9)+1/3(x+9)
1/3x=11/6(x+9)
x=2.
解题方法:裂项法.

公式:1/n(n+3)=1/3[1/n-1/(n+3)]
1/x(x+3)+1/(x+3)(x+6)+1/(x+6)(x+9)=3/(2x+18)
1/3[1/x-1/(x+3)+1/(x+3)-1/(x+6)+1/(x+6)-1/(x+9)]=3/(2x+18)
1/3[1/x-1/(x+9)]=3/2(x+9)
2(x+9)-2x=9x
9x=18
x=2