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

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/02 18:56:38
先化简,再求值:(x-x/x+1)÷(1+1/x²-1),其中x=根号2 +1

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

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

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

原式=[(x²+x)/(x+1)-x/(x+1)]÷[(x²-1)/(x²-1)+1/(x²-1)]
=[(x²+1)/x+1]÷[x²/(x²-1)]
=[(x²+1)/x+1]×[(x²-1)/x²]
=(x²+1)(x...

全部展开

原式=[(x²+x)/(x+1)-x/(x+1)]÷[(x²-1)/(x²-1)+1/(x²-1)]
=[(x²+1)/x+1]÷[x²/(x²-1)]
=[(x²+1)/x+1]×[(x²-1)/x²]
=(x²+1)(x-1)/x²
=[(根号2 +1)^2+1]×根号2/(根号2 +1)^2
=(4+2×根号2)]×根号2/(3+2×根号2)
=(4+4×根号2)(3-2×根号2)=4×根号2-4

收起