解方程:1/x-4-2/x-3=3/x-2-4/x-1

1/(x-4)-2/(x-3)=3/(x-2)-4/(x-1)
移项：1/(x-4)+4/(x-1)=3/(x-2)+2/(x-3)
通分：[x-1+4(x-4)]/[(x-4)(x-1)]=[3(x-3)+2(x-2)]/[(x-2)(x-3)]
(5x-17)/(x²-5x+4)=(5x-13)/(x²-5x+6)
去分母：(5x-17)(x²-5x+6)=(5x-13)(x²-5x+4)
30x-17(x²-5x)-102=20x-13(x²-5x)-52
4(x²-5x)-10x+50=0
2x²-15x+25=0
(2x-5)(x-5)=0
x=2.5,5
经检验,它们都是原方程的根.