用换元法解分式方程(x/x-1)-5(x/x-1)-6=0

问题描述:

用换元法解分式方程(x/x-1)-5(x/x-1)-6=0

设t=x/(x-1),
(x/x-1)^2-5(x/x-1)-6 = 0
t^2-5t-6 = 0
(t+1)*(t-6)=0
t1=-1
t2=6
代入和t1=-1 到t=x/(x-1)中,
x/(x-1)=-1
解得 x1=1/2
代入和t2=6 到t=x/(x-1)中,
x/(x-1)=6
解得 x2=6/5