1/x(x+2)+1/(x+2)(x+4)+...1/(x+8)(x+10)=5/24
½×[1/x-1/(x+2)]+½[1/(x+2)-1/(x+4)]+……+½[1/(x+8)-1/(x+10)]=5/24
1/x-1/(x+2)+1/(x+2)-1/(x+4)+……+1/(x+8)-1/(x+10)=5/12
1/x-1/(x+10)=5/12
12(x+10)-12x=5x(x+10)
12x+120-12x=5x²+50x
5x²+50x-120=0
x²+10x-24=0
(x-4)(x-6)=0
x1=4,x2=6