82问答网 > 你会解方程x⼀x-1-x-1⼀x-2=x-3⼀x-4-x-4⼀x-5

你会解方程x⼀x-1-x-1⼀x-2=x-3⼀x-4-x-4⼀x-5

是不是无解？

2024-12-01 18:12:57

推荐回答（5个）

回答1：

先通分再求解
(x^2-2x-x^2+2x-1)/(x-1)/(x-2)=(x^2-8x+15-x^2+8x-16)/(x-4)/(x-5)
1/(x-1)/(x-2)=1/(x-4)/(x-5)
x^2-9x+20=x^2-3x+2
6x=18
x=3

回答2：

x/(x-1)-(x-1)/(x-2)=(x-3)/(x-4)-(x-4)/(x-5) 通分
(x^2-2x-x^2+2x-1)/(x-1)/(x-2)=(x^2-8x+15-x^2+8x-16)/(x-4)/(x-5)
1/(x-1)/(x-2)=1/(x-4)/(x-5)
x^2-9x+20=x^2-3x+2
6x=18
x=3

回答3：

x/(x-1)-(x-1)/(x-2)=(x-3)/(x-4)-(x-4)/(x-5)
(x^2-2x-x^2+2x-1)/(x-1)/(x-2)=(x^2-8x+15-x^2+8x-16)/(x-4)/(x-5)
1/(x-1)/(x-2)=1/(x-4)/(x-5)
x^2-9x+20=x^2-3x+2
6x=18
x=3

回答4：

左右通分：1/[(x-1)*(x-2)]=1/[(x-4)*(x-5)]
(x-1)*(x-2)=1/(x-4)*(x-5)
x=3
检验一下ok

回答5：