Question

先化简，再求值：〔（x-1）/x—（x-2）/x+1 〕÷〔2x²-x/x²+2x+1〕其中x满足x²-x-1=0

Answer 1

〔（x-1）/x—（x-2）/x+1 〕÷〔2x²-x/x²+2x+1〕
=【（x-1)（x+1)/x(x+1)-x(x-2)/x(x+1)】÷【x(2x-1)/(x+1)²〕
=【（x-1)（x+1)-x(x-2)】/x(x+1)*【(x+1)²/x(2x-1)】
=(2x-1)/x(x+1)*【(x+1)²/x(2x-1)】
=(x+1)/x²
因为x²-x-1=0，所以x²=x+1
所以原式=(x+1)/x²=1

Answer 2

[(x-1)/x-(x-2)/(x+1)]÷(2x^2-x)/(x^2+2x+1)
=[(x-1)(x+1)/x(x+1)-x(x-2)/x(x+1)]×(x+1)^2/x(2x-1)
=(x^2-1-x^2+2x)/x(x+1)×(x+1)^2/x(2x-1)
=(2x-1)/x(x+1)×(x+1)^2/x(2x-1)
=(x+1)/(x^2)

x^2-x-1=0
x^2=x+1

原式
=(x+1)/(x^2)
=(x^2)/(x^2)
=1

Answer 3

x为正负1

因为1乘以任何数都等于它本身。