Question

你会解方程x/(x-1) -(x-1)/(x-2) =(x-3)/(x-4) -(x-4)/(x-5)吗

Answer 1

x/(x-1) -(x-1)/(x-2) =(x-3)/(x-4) -(x-4)/(x-5)
[1+1/(x-1)]-[1+1/(x-2)]=[1+1/(x-4)]-[1+1/(x-5)]
1/(x-1)-1/(x-2)=1/(x-4)-1/(x-5)
1/(x-1)+1/(x-5)=1/(x-4)+1/(x-2)
[(x-1)+(x-5)]/[(x-1)(x-5)]=[(x-2)+(x-4)]/[(x-2)(x-4)]
(2x-6)/(x^2-6x+5)=(2x-6)/(x^2-6x+8)
2x-6=0或x^2-6x+5=x^2-6x+8
x=3

Answer 2

x/(x-1) -(x-1)/(x-2) =(x-3)/(x-4) -(x-4)/(x-5)
化简，得
1/(x-1) -1/(x-2) =1/(x-4) -1/(x-5)
-1/(x-1)(x-2) =-1/(x-4) (x-5)
(x-1)(x-2) =(x-4) (x-5)
x²-3x＋2=x²-9x＋20
6x=18
x=3
经检验x=3是方程的根。

Answer 3

[X(X-2)-（X-1)(x-1）]（x-4)(x-5)-[（x-3)(x-5)-(X-4)(X-4)](X-1)(X-2)=0
（x-4)(x-5)-(X-1)(X-2)=0
-9X+20+3X-2=0
6X=18
X=3