作业帮一道分式方程.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.要具体.
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/28 04:48:11
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.要具体.
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.
要具体.
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.要具体.
X=4
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,同时去掉-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的要求.
(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/(x-6)]...
全部展开
(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/(x-6)]
1+1/(x-2)-1-1/(x-3)=1+1/(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(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
收起
先共同去分母
解出
代入分母中，分母不等于0
(X-1)/(X-2)-(X-2)/(X-3)=(X-4)/(X-5)-(X-5)/(X-6)
[X^2-4X+3-X^2+4X-4]/[(X-2)(X-3)] =-1/[(X-5)(X-6)]
X=4