解: 1/(x-1)+1/(x-4)=1/(x-2)+1/(x-3)
(x-4+x-1)/(x-1)(x-4)=(x-3+x-2)/(x-2)(x-3)
(2x-5)/(x-1)(x-4)=(2x-5)/(x-2)(x-3)
因为(x-1)(x-4)=x^2-5x+4
(x-2)(x-3)=x^2-5x+6
所以 (x-1)(x-4)不等于(x-2)(x-3)
因此 只有2x-5=0
解得 x=5/2
