观察下列各等式1/(1×2)=1-1/2,1/(2×3)=1/2-1/3,1/(3×4)=1/3+1/4,……
问题描述：
观察下列各等式1/(1×2)=1-1/2,1/(2×3)=1/2-1/3,1/(3×4)=1/3+1/4,……
利用规律计算1/x(x-1)+1/(x-1)(x-2)+1/(x-2)(x-3)
答
裂项1/(x-1)-1/x+1/x-2-1/(x-1)...+1/(x-3)=1/(x-1)+1/(x-3)=(2x-4)/(x-1)(x-3)