(x-1分之x)的平方-5(x-1分之x)+6=0 解方程

[(x-1)分之x]²-5[(x-1)分之x]+6=0
[(x-1)分之x-2][(x-1)分之x-3]=0
[(x-1)分之x-(x-1)分之2(x-1)][(x-1)分之x-(x-1)分之3(x-1)]=0
{(x-1)分之[x-2(x-1)]}{(x-1)分之[x-3(x-1)]}=0
[(x-1)分之(-x+2)][(x-1)分之(-2x+3)]=0
[-(x-1)分之(x-2)][-(x-1)分之(2x-3)]=0
(x-1)²分之[(x-2)(2x-3)]=0
(x-2)(2x-3)=0
x1=2,x2=2分之3

地税局办贷款深V

令t=x-1/x

则如图：

令[x/(x-1)]=t，则 t²-5t+6 = 0，得t = 2或3.
若t=2（即[x/(x-1)=2，则x=2，若t=3，则x=3/2，所以方程的解为x=2或x=3/2