用换元法解方程3x^2/(x^2-4x+4)-8x/(x-2)-3=0

Question

用换元法解方程3x^2/(x^2-4x+4)-8x/(x-2)-3=0

Answer 1

3x^2(x-2)^2-8x/(x-2)-3=0
令a=x/(x-2)
3a^2-8a-3=0
(3a+1)(a-3)=0
a=-1/3,a=3
x/(x-2)=-1/3
x-2=-3x
x
=1/2
x/(x-2)=3
x=3x-6
x=3
所以x=1/2,x=3