Question

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

如题。要有过程。谢谢

Answer 1

[(x-1)+1]/(x-1)-[(x-2)+1]/(x-2)=[(x-4)+1]/(x-4)-[(x-5)+1]/(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)(x-2)=-1/(x-4)(x-5)
∴(x-4)(x-5)=(x-1)(x-2)
x²-9x+20=x²-3x+2
6x=18
x=3
检验：