解方程:1/[x(x+1)]+1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+9)(x+10)=5/12
问题描述：
解方程:1/[x(x+1)]+1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+9)(x+10)=5/12
答
1/[x(x+1)]+1/(x+1)(x+2)+1/(x+2)(x+3)+.+1/(x+9)(x+10)=5/12
1/x-1/(x+1)+1/(x+1)-1/(x+2)+...+1/(x+9)-1/(x+10)=5/12;
1/x-1/(x+10)=5/12;
12(x+10)-12x=5x(x+10);
120=5x²+50x;
x²+10x-24=0;
(x+12)(x-2)=0;
x=2或x=-12；
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