x-2分之1-x-3分之1=x-6分之1-x-7分之1

1/(x-2) -1/(x-3)=1/(x-6) -1/(x-7) 方程两边分别通分
(x-3)/[(x-2)(x-3)] -(x-2)/[(x-2)(x-3)] =(x-7)/[(x-6)(x-7)] -(x-6)/[(x-6)(x-7)]
-1/[(x-2)(x-3)] =-1/[(x-6)(x-7)] 方程两边同时乘最简公分母(x-2)(x-3)(x-6)(x-7)
(x-6)(x-7)=(x-2)(x-3) 方程两边展开
x²-13x+42=x²-5x+6 移项合并
-8x=-36 系数化1
x=4.5
检验：把x=4.5代入最简公分母
(x-2)(x-3)(x-6)(x-7)≠0
所以 x=4.5是原方程的根