先化简，再求值x+2/2x^2-4x除以（x-2+8x/x-2），其中x=根号2-1
先化简，再求值x+2/2x^2-4x除以（x-2+8x/x-2），其中x=根号2-1
先化简，再求值x+2/2x^2-4x除以（x-2+8x/x-2），其中x=根号2-1
解：
原式=(x+2)/2x(x-2)÷【(x^2-4+8x)/(x-2)】
=(x+2)/2x(x-2)*(x-2)/(x^2+8x-4)
=(x+2)/2x(x^2+8x-4)
=(√2-1+2)/2*(√2-1)(3-2√2+8√2-8-4)
=(√2+1)/(42-30√2)
先化简再求值 x+2/2x²-4x ÷ (x-2+8x/x-2).其中x=√2 -1.
(x+2)/(2x²-4x )÷ [(x-2)+(8x/(x-2)]
= [(x+2)/2x(x-2 )]÷ [(x-2)^2+8x]/(x-2)
= [(x+2)/2x(x-2 )]*[(x-2)/(x+2)^2]
=1/x(x+2)
x=√2 -1.
原式=1/x(x+2)
=1/[(√2 -1)(√2 +1)]
=1/(2-1)
=1
先化简,再求值:x+2/2x-4x÷(x-2+8x/x-2),其中x满足x=2x-1
x=2x-1
2x-x=1
x=1
x+2/2x-4x÷(x-2+8x/x-2)
=(x+2)/(-2x) ÷ (x²-4x+4+8x)/(x-2)
=(x+2)/(-2x) ÷ (x²+4x+4)/(x-2)
=(x+2)/(-2x) ÷ (x+2)²/(x-2)
=(x+2)/(-2x) *(x-2)/ (x+2)²
=(x-2)/(-2x)(x+2)
当x=1
原式=(x-2)/(-2x)(x+2)=-1/(-2×3)=1/6
先化简再求值[(x+2)/(2x²-4x）][x-2+(x-2)/(8x)] 其中x=根号2-1
[(x+2)/(2x²-4x）][x-2+(x-2)/(8x)]
=(x+2)(x-2)[1+1/(8x)]/[2x(x-2)]
=(x+2)(x-2)(8x+1)/[16x²(x-2)]
=(x+2)(8x+1)/(16x²)
=（√2-1+2）（8√2-8+1）/[16（√2-1）²]
=（√2+1）（8√2-7）（√2+1）²/16
=（16+√2-7）（3+2√2）/16
=（9+√2）（3+2√2）/16
=（31+21√2）/16
先化简，再求值：（x+2/x^2-2x-x-1/x^2-4x+4)除以x^2-16/x^2+4x，其中x=2+根号
根号几啊？
原式=[(x+2)/x(x-2)-(x-1)/(x-2)²]÷(x+4)(x-4)/x(x+4)
=(x²-4-x²+x)/x(x-2)²*x/(x-4)
=(x-4)/x(x-2)²*x/(x-4)
=1/(x-2)²
先化简，再求值：x/(x^2-2x+1)除以((x+1)/(x^2-1)+1),其中x=根号2+1.
原式=x/(x-1)+1=x/(x-1)²÷（x+1）/（x+1）（x-1）+1=2x /(x-1)。当x=根2+1时，原式=2+根2/2.。
先化简再求值:1/（x+2）-（x^2+2x+1）/（x-2）÷（x^2-1）/（x-1）,其中x=（根号2）-2
1/（x+2）-（x^2+2x+1）/（x-2）÷（x^2-1）/（x-1）
=1/（x+2）-（x+1）²/（x-2）÷（x-1）(x+1)/（x-1）
=1/(x+2)-(x+1)/(x-2)
=(x-2-x²-3x-2)/(x+2)(x-2)
=[-(x+1)²-3]/(x+2)(x-2)
=[-(根号2-1)²-3]/(2-4根号2)
=(-1+5根号2)/7
先化简,再求值:(x-2)/(x^2-1)÷(2x+2)/(x^2+2x+1)+1/(x-1),其中x=根号2+1
(x-2)/(x^2-1)÷(2x+2)/(x^2+2x+1)+1/(x-1)
=(x-2)/(x-1)(x+1)÷2(x+1)/(x+1)²+1/(x-1)
=(x-2)/(x-1)(x+1)*(x+1)/2+1/(x-1)
=(x-2)/2(x-1)+1/(x-1)
=[(x-2)+2]/2(x-1)
=x/2(x-1)=(√2+1)/2(√2+1-1)=(2+√2)/4
先化简再求值:(1-1/x)/(x^2-2x+1)/(x^2-1),其中x=根号2
(1-1/x)/(x^2-2x+1)/(x^2-1)
=[(x-1)/x]/[(x+1)(x+1)]/[(x+1)(x-1)]
=[(x-1)/x]/[(x+1)/(x-1)]
=1/x/[(x+1)
=1/[x(x+1)]
=1/(2+根号2)
=(2-根号2)/[(2+根号2)(2-根号2)]
=(2-根号2)/2
x^2-4x / x^2-8x+16 , 其中 x=5 . 先化简 再求值
x^2-4x / x^2-8x+16
=x(x-4)/(x-4)^2
=x/(x-4)
=5/(5-4)
=5
