230问答网 > 解方程(x-2)⼀(x-3)-(x-3)⼀(x-4)=(x-5)⼀(x-6)-(x-6)⼀(x-7)

解方程(x-2)⼀(x-3)-(x-3)⼀(x-4)=(x-5)⼀(x-6)-(x-6)⼀(x-7)

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

2024-12-16 10:22:19

推荐回答（3个）

回答1：

((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.

回答2：

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

回答3：

(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