Question

一道分式方程。X-2分之X-1减X-3分之X-2=X-5分之X-4减X-6分之X-5。

Answer 1

X=4
解：
原式=(X-1)/(X-2)-(X-2)/(X-3)=(X-4)/(X-5)-(X-5)/(X-6)
左边
通分
=[X^2-4X+3-X^2+4X-4]/[(X-2)(X-3)]
=
-1/[(X-2)(X-3)]
右边通分=-1/[(X-5)(X-6)]
等式两边相等坦缺，同时去掉基磨-1，
原式可以
化简
为：
X^2-11X+30=X^2-5X+6
即：
6X=24
X=4
满足
题设
分母
不等于零搏信斗的要求。

Answer 2

(x-1)/(x-2)-(x-2)/(x-3)=(x-4)/(x-5)-(x-5)/(x-6)
(x-2+1)/(x-2)-(x-3+1)/(x-3)=(x-5+1)/(x-5)-(x-6+1)/(x-6)
[(x-2)/(x-2)+1/(x-2)]-[(x-3)/(x-3)+1/(x-3)]=[(x-5)//(x-5)+1/(x-5)]-[(x-6)/(x-6)+1/唤宽(x-6)]
1+1/(x-2)-1-1/(x-3)=1+1/和清亮(x-5)-1-1/(x-6)
1/(x-2)-1/(x-3)=1/(x-5)-1/(x-6)
[(x-3)-(x-2)]/[(x-2)(x-3)]=(x-6)-(x-5)]/[(x-5)(x-6)]
-1/[(x-2)(x-3)]=-1/[(x-5)(x-6)]
所以正野(x-2)(x-3)=(x-5)(x-6)
所以x^2-5x+6=x^2-11x+30
6x=24
x=4
分式方程要检验
经检验
x=4是方程的解