解方程(x-2)/(x-3)-(x-3)/(x-4)=(x-5)/(x-6)-(x-6)/(x-7)

来源：学生作业帮助网 编辑：作业帮 时间：2024/04/27 19:21:07
解方程(x-2)/(x-3)-(x-3)/(x-4)=(x-5)/(x-6)-(x-6)/(x-7)

解方程(x-2)/(x-3)-(x-3)/(x-4)=(x-5)/(x-6)-(x-6)/(x-7)
解方程(x-2)/(x-3)-(x-3)/(x-4)=(x-5)/(x-6)-(x-6)/(x-7)

解方程(x-2)/(x-3)-(x-3)/(x-4)=(x-5)/(x-6)-(x-6)/(x-7)
((X-2)(X-4)-(X-3)^2)/(X-3)(X-4)=((X-5)(X-7)-(X-6)^2)/(X-6)(X-7),
-1/(X^2-7X+12)=-1/(X^2-13X+42),
6X=30,
X=5.

左右分别通分
得
-1/(x-3)(x-4)=-1/(x-6)(x-7)
所以 原方程化为
(x-3)(x-4)=(x-6)(x-7)
即
x^2-7x+12=x^2-13x+42
6x=30
x=5

(x-2)/(x-3)-(x-3)/(x-4)=(x-5)/(x-6)-(x-6)/(x-7)
(x-3+1)/(x-3)-(x-4+1)/(x-4)=(x-6+1)/(x-6)-(x-7+1)/(x-7)
1/(x-3)-1/(x-4)=1/(x-6)-1/(x-7)
-1/[(x-3)*(x-4)]=-1/[(x-6)*(x-7)]
(x-3)*(x-4)=(x-6)*(x-7)
x^2-7x+12=x^2-13x+42
6x=30
x=5
经代入公分母(x-3)*(x-4)*(x-6)*(x-7)＝4≠0，合理

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