题目
已知x2-4x+1=0,求x2/(x-1)-(1+1/(x2-x))的值
提问时间：2020-11-03
答案
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
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
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