x-2分之1-x-3分之1=x-6分之1-x-7分之1
1个回答

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