x^2-4x+1=0
x^2=4x-1
x^2/(x-1)-[1+1/(x^2-x)]
=(4x-1)/(x-1)-(x^2-x+1)/(x^2-x)
=(4x-1)/(x-1)-(4x-1-x+1)/(4x-1-x)
=(4x-1)/(x-1)-3x/(3x-1)
=[(4x-1)(3x-1)-3x(x-1)]/(x-1)(3x-1)
=(9x^2-4x+1)/(3x^2-4x+1)
=[9(4x-1)-4x+1]/[3(4x-1)-4x+1)
=(32x-8)/(8x-2)
=8(4x-1)/2(4x-1)
=4