Question

先化简再求值 （1+x）分之（x²+2x）÷{x-（x+1）分之2}-1,其中x=根号2+1分之1

Answer 1

x=1/(√2+1)=√2-1

原式=x(x+2)/(x+1)÷(x²+x-2)/(x+1)-1
=x(x+2)/(x+1)*(x+1)/(x+2)(x-1)-1

=x/(x-1)-1

=(x-x+1)/(x-1)
=1/(x-1)
=1/(√2-1-1)
=(√2+2)/(2-4)
=-(√2+2)/2

Answer 2

您好：

（x²+2x）/(1+x)÷{x-2/（x+1）}-1
=x(x+2)/(x+1) ÷[(2x+2-2)]/(x+1) -1
=x(x+2)/(x+1)÷ 2x/(x+1)-1
=(x+2)/2-1
=1/2x+1-1
=1/2x
=1/2*1/(√2+1)
=1/2*(√2-1)/(√2+1)(√2-1)
=1/2(√2-1)/(2-1)
=1/2(√2-1)

不明白，可以追问如有帮助，记得采纳，谢谢 祝学习进步！

追问

[(2x+2-2)]/(x+1)，这一步没看懂，不是应该化成(x²+x-2)/x+1吗？

追答

哦 对的，我看错了

x-（x+1）分之2 通分
=[x（x+1）-2]/(x+1)
=(x²+x-2)/(x+1)
=（x+2）(x-1)/(x+1)

（x²+2x）/(1+x)÷{x-2/（x+1）}-1
=x(x+2)/(x+1) ÷[(2x+2-2)]/(x+1) -1
=x(x+2)/(x+1)÷ (x+2)(x-1)/(x+1)-1
=x/(x-1)-1
=(x-x+1)/(x-1)
=1/(x-1)
=1/（√2+1-1）
=1/√2
=√2/2

追问

1/（√2+1-1）这步错了吧，x的值不是（√2+1）吧！
x=根号2+1分之1

Answer 3

原式=x(x+2)/(x+1)÷[(x+2)(x-1)/(x+1)]-1=x/(x-1)
x=1/(√2+1)=√2-1
原式=(√2-1)/(√2-2)=-√2/2