Question

分式（解方程）1道 （1）(x-1)/(x-2)=1/(x-2)

Answer 1

(x-1)/(x-2)=1/(x-2)

x-1=1,x=2

但x-2使分母为0,2为增根

∴原方程无解.

也可这样分析:

(x-1)/(x-2)=[(x-2)+1]/(x-2)=(x-2)/(x-2)+1/(x-2)

=1+1/(x-2)≠1/(x-2)

∴原方程无解.