Question

1/x(x+2)+1/(x+2)(x+4)+...+1/(x+8)(x+10)=5/24x

Answer 1

1/x(x+2)+1/(x+2)(x+4)+...+1/(x+8)(x+10)=5/24

1/2*[1/x-1/(x+2)+1/(x+2)-1/(x+4)+...+1/(x+8)-1/(x+10)]=5/24

1/2*[1/x-1/(x+10)]=5/24

1/x-1/(x+10)=5/12

10/x(x+10)=5/12

2/x(x-10)=1/12

x(x-10)==24

x²-10x-24=0

(x-12)(x+2)=0

x=12 x=-2

经检验x=-2是增根

所以x=12是原方程的根