Question

先化简,再求值:(x²-1/x²-2x+1)-(x²-2x/x-2)÷x,其中x=√5-1

先化简,再求值:(x²-1/x²-2x+1)-(x²-2x/x-2)÷x,其中x=√5-1

Answer 1

解：化简所求式=(x+1)(x-1)/(x-1)²-x(x-2)/(x-2)·1/x
=(x+1)/(x-1)-1
当x=√5-1时
所求式=(√5-1+1)/(√5-1-1)-1
=√5/(√5-2)-1
=√5(√5+2)/(√5-2)(√5+2)-1
=5-2√5-1
=4-2√5

Answer 2

您好：

(x²-1/x²-2x+1)-(x²-2x/x-2)÷x
=（x+1）（x-1）/(x-1)²-x(x-2)/(x-2)÷x
=（x+1）/(x-1)-1
=(x+1-x+1)/(x-1)
=2/(x-1)
=2/(√5-1-1)
=2/(√5-2)
=2(√5+2)/(5-4)
=2√5+4

如果本题有什么不明白可以追问，如果满意记得采纳
如果有其他问题请采纳本题后另发点击向我求助，答题不易，请谅解，谢谢。
祝学习进步！

Answer 3

(x²-1/x²-2x+1)-(x²-2x/x-2)÷x
=(x+1)(x-1)/(x-1)^2-x(x-2)/x(x-2)
=(x+1)/(x-1)-1
=(x+1-x+1)/(x-1)
=2/(x-1)
=2/(√5-1-1)
=2/(√5-2)
=2(√5+2)/(√5-2)(√5+2)
=2√5+4

不懂可追问
满意请采纳
谢谢

Answer 4

原式=[(x+1)(x-1)/(x-1)²]-[x(x-2)/(x-2)]÷x
=[(x+1)/(x-1)]-x÷x
=1+[2/(x-1)]-1
=2/(x-1)
=2/(√5-2)
=2(√5+2)

Answer 5

上面都是正确的，但只是其中一种解答