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.

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：