分式方程1/[x(x+1)]+1/[(x+1)(x+2)]+1/[(x+2)(x+3)]+...+1/[(x+9)(x+

来源：学生作业帮编辑：作业帮分类：综合作业时间：2024/05/05 12:23:41

分式方程1/[x(x+1)]+1/[(x+1)(x+2)]+1/[(x+2)(x+3)]+...+1/[(x+9)(x+10)]=5/12

即1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+...+1/(x+9)-1/(x+10)=5/12
1/x-1/(x+10)=5/12
两边乘12x(x+10)
120=5x²+50x
x²+10x-24=0
(x+12)(x-2)=0
x=-12,x=2

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