解方程：1/x(x+2)+1/(x+2)(x+4)+……+1/(x+8)(x+10)=5/24

1/2x-1/2(x+2)+1/2(x+2)-1/2(x+4)+……+1/2(x+8)-1/2(x+10)=5/24
1/2x-1/2(x+10)=5/24
10/x(x+10)=5/12
x=2或x=-12

x=-2或12
1/x(x+2)=(1/x-1/(x+2))/2

1/x(x+2)+1/(x+2)(x+4)+……+1/(x+8)(x+10)=5/241/(2x)-1/{2(x+2)) + 1/{2(x+2)}-1/{2(x+4)} +……+1/{2(x+8)} - 1/{2(x+10)} = 5/241/(2x)-1/{2(x+10)} = 5/241/x-1/(x+10) = 5/1210/{x(x+10)} = 5/122/{x(x+10)} =...

1/x-1/(x+2)=2/x(x+2)
则：1/x(x+2)=1/2[1/x-1/(x+2)]
同理，其它项也可以如此变形，所以：
1/x(x+2)+1/(x+2)(x+4)+……+1/(x+8)(x+10)
=1/2[1/x-1/(x+2)+1/(x+2)-1/(x+4)+......+1/(x+6)-1/(x+8)+1/(x+8)-1/(x+10)]
=1/2[1/x-1/(x+10)]
=5/24
要解的就是1/2[1/x-1/(x+10)]=5/24
10/x(x+10)=5/12
(x+12)(x-2)=0
x=-12或x=2