1/(x-1)-1/(x-2)=1/(x-3)-1/(x-4)
1/(x-1)+1/(x-4)=1/(x-2)+1/(x-3)
通分
(2x-5)/(x²-5x+4)=(2x-5)/(x²-5x+6)
(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