已知x2-4x+1=0,求x2/(x-1)-(1+1/(x2-x))的值

来源:学生作业帮助网 编辑:作业帮 时间:2018/02/21 09:11:28
已知x2-4x+1=0,求x2/(x-1)-(1+1/(x2-x))的值已知x2-4x+1=0,求x2/(x-1)-(1+1/(x2-x))的值已知x2-4x+1=0,求x2/(x-1)-(1+1/(

已知x2-4x+1=0,求x2/(x-1)-(1+1/(x2-x))的值
已知x2-4x+1=0,求x2/(x-1)-(1+1/(x2-x))的值

已知x2-4x+1=0,求x2/(x-1)-(1+1/(x2-x))的值
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/(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