先化简,再求值;(x分之x-1—x+1分之x-2)÷x的平分+2x+1分之2x的平分-x,其中x满足x²-x-1=0

题目

先化简,再求值;(x分之x-1—x+1分之x-2)÷x的平分+2x+1分之2x的平分-x,其中x满足x²-x-1=0

答案

x^2-x-1=0
x^2=x+1
(x分之x-1—x+1分之x-2)÷x的平分+2x+1分之2x的平分-x
=((x-1)(x+1)-x(x-2))/x(x+1)÷(x(2x-1)/(x+1)^2)
=((x^2-1-x^2+2x)/x(x+1))÷(x(2x-1)/(x+1)^2)
=(2x-1)/x(x+1) * (x+1)^2/x(2x-1)
=(x+1)/x^2
=x^2/x^2
=1