Question

1/x-1-1/x-2=1/x-3-1/x-4

Answer 1

先在等式两边分别通分，得:
(x-2)-(x-1)
(x-4)-(x-3)
分数线------
=
------
(x-1)(x-2)
(x-3)(x-4)
-1
-1
------
=
------
(x-1)(x-2)
(x-3)(x-4)
(x-3)(x-4)
=
(x-1)(x-2)
x^2-7x+12
=
x^2-3x+2
-4x
=
-10
x
=
2.5
检验:当x=2.5时，x-1≠0、x-2≠0、x-3≠0、x-4≠0.
∴x=2.5是原分式方程的解。
(全手打，求楼主采纳!)

Answer 2

1/(x-1)-1/(x-2)=1/(x-3)-1/(x-4) ; x≠1,2,3,4
-1/[(x-1)(x-2)]=-1/[(x-3)(x-4)]
(x-1)(x-2)=(x-3)(x-4)
x^2-3x+2=x^2-7x+12
4x=10
x=5/2