[x/(x-1)]^2-2[x/(1-x)]-3=0[x/(x-1)]^2+2[x/(x-1)]-3=0设t=x/(x-1),则x=t/(t-1)t^2+2t-3=0(t-1)(t+3)=0t₁=1,t₂=-3 t=1为增根,舍去t=-3时,x=-3/(-3-1)=3/4原方程的解为x=3/4