x^2-5x+1=0
所以x^2=5x-1
-5x+1=-x^2
x^2/(x-1)-[1+1/(x^2-x)]
=(5x-1)/(x-1)-1-1/(5x-1-x)
=(5x-1)/(x-1)-1-1/(4x-1)
=[(5x-1)(4x-1)-(x-1)(4x-1)-(x-1)]/(x-1)(4x-1)
=(20x^2-9x+1-4x^2+5x-1-x+1)/(4x^2-5x+1)
=(16x^2-5x+1)/(4x^2-5x+1)
=(16x^2-x^2)/(4x^2-x^2)
=15x^2/3x^2
=5