令x-1/x=t,则
t^2-t-2=0
t=-1,t=2
(1)x-1/x=-1
x=1/2
(2)x-1/x=2
x=-1
(x-1)^2/x^2-(x-1)/(x-2)=0
左边提取公因式x-1：
(x-1) { (x-1)/x^2 - 1/(x-2) } = 0
(x-1) { (x-1)(x-2) - x^2 } / {x^2(x-2) } = 0
(x-1) (x^2-3x+2 - x^2) / {x^2(x-2) } = 0
(x-1) (-3x+2) / {x^2(x-2) } = 0
x-1=0，或-3x+2=0
x1=1，x2=2/3
(x-1)^2*(x-2)-(x-1)*x^2=0
(x^3-2x^2+x-2x^2+4x-2)-(x^3-x^2)=0
(x^3-4x^2+5x-2)-x^3+x^2=0
5x-2-3x^2=0
(3x-2)(x-1)=0
x=2/3或x=1
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