Question

已知x2-4x+1=0,求x2/(x-1)-(1+1/(x2-x))的值

Answer 1

x2/(x-1)-(1+1/(x2-x))，将式子同分得：（x3-x2+x-1）/（x2-x）；
继续化简得：（x-1）（x2+1）/(x-1)x，得（x2+1）/x，
又由已知得：x2=4x-1，代入得：（4x-1+1）/x=4，
结果：：4

Answer 2

x2-4x+1=0
x2+1=4x
x2/(x-1)-(1+1/(x2-x))
=x^2/(x-1)-(x^2-x+1)/(x^2-x)
=x^2/(x-1)-(4x-x)/(x^2-x)
=x^3-3x/(x^2-x)
=x(x^2-3)/x(x-1)
=(4x-1-3)/(x-1)
=4(x-1)/(x-1)
=4