Question

1除以x-1 - （除以x-2）等于1除以x-3-（1除以x-4）

Answer 1

1/(x-1)+1/(x-4)-[1/(x-2)+1/(x-3)]=0
通分
(2x-5)/(x²-5x+4)-(2x-5)/(x²-5x+6)=0
(2x-5)[1/(x²-5x+4)-1/(x²-5x+6)]=0
x²-5x+4≠x²-5x+6
所以1/(x²-5x+4)-1/(x²-5x+6)≠0
所以2x-5=0
x=5/2
分式方程要检验
经检验，x=5/2是方程的解

Answer 2

1/(x-1)-1/(x-2)=1/(x-3)-1/(x-4)
1/(x-1)+1/(x-4)=1/(x-3)+1/(x-2)
(x-4+x-1)/[(x-1)(x-4)]=(x-2+x-3)/[(x-2)(x-3)]
(2x-5)/(x²-5x+4)=(2x-5)/(x²-5x+6)
x²-5x+4≠x²-5x+6
所以2x-5=0
x=2.5
经检验，x=2.5是原方程的根