已知a^2+2a-1=0,求分式[（a-2）/(a^2+2a)-(a-1)/(a^2+4a+4)]/(a-4)/(a+2）的值。
已知a^2+2a-1=0,求分式[（a-2）/(a^2+2a)-(a-1)/(a^2+4a+4)]/(a-4)/(a+2）的值。
解：
因为a^2+2a-1=0,
所以a^2+2a=1
所以[(a-2)/(a^2+2a)-(a-1)/(a^2+4a+4)]/[(a-4)/(a+2)
=[(a-2)/a(a+2)-(a-1)/(a+2)^2]*[(a+2)/(a-4)]
=[(a-2)(a+2)/a(a+2)^2-a(a-1)/a(a+2)^2]*[(a+2)/(a-4)]
=[(a^2-4-a^2+a)/a(a+2)^2]*[(a+2)/(a-4)]
=[(a-4)/a(a+2)^2]*[(a+2)/(a-4)]
=1/a(a+2)
=1/(a^2+2a)
=1/1
=1.
已知a²+2a-√3=0，求代数式[（a-2)/（a²+2a)-(a-1)/（a²+4a+4）]÷（a-4)/(a+2)
由[（a-2)/（a（a+2)-（a-1)/（a+2)²]÷（a-4)/（a+2)
=[（a-2)(a+2)/a(a+2)²-a(a-1)/a(a+2)²
=(a-4)/a(a+2)²×(a+2)/(a-4)
=1/a(a+2)
∵a²+2a=√3,
∴1/a(a+2)
=1/(a²+2a)
=1/√3
=√3/3.
已知a^2+2a-1=0,求(a^2-16)/(a^3+4a^2+4a)乘以(a+2)/(a-4)除以(a+4)+3
(a^2-16)/(a^3+4a^2+4a)乘以(a+2)/(a-4)除以(a+4)+3
=[(a+4)(a-4)/a(a+2)^2]*[(a+2)/(a-4)]/(a+4)+3
=1/a(a+2)+3
=1/(a^2+2a)+3
已知a^2+2a-1=0 a^2+2a=1
则原式=1+3
=4
已知a^2+2a-2012=0，求代数式[(a-2)/(a^2+2a)-(a-1)/(a^2+4a+
[(a-2)/(a^2+2a)-(a-1)/(a^2+4a+4)]÷(a-4)/(a+2)
=[(a-2)/a(a+2)-(a-1)/(a+2)^2]x(a+2)/(a-4)
=[(a-2)(a+2)/a(a+2)^2-a(a-1)/a(a+2)^2]x(a+2)/(a-4)
=(a^2-4-a^2+a)/a(a+2)^2x(a+2)/(a-4)
=(a-4)/a(a+2)^2x(a+2)/(a-4)
=1/a(a+2)
=1/(a^2+2a)
=1/2012
(a-2）/(a^2+2a)减（a-1）/(a^+4a+4)的差除a-4/a+2 是x^2+2x-1=0
x=a
所以a²+2a-1=0
a²+2a=1
原式=[(a-2)/a(a+2)-(a-1)/(a+2)²]×(a+2)/(a-4)
=(a²-4-a²+a)/a(a+2)²×(a+2)/(a-4)
=(a-4)/a(a+2)²×(a+2)/(a-4)
=1/(a²+2a)
=1
若a=1/2，求（a^2-4/a^-4a+4-1/a-2）÷a+1/a+2的值
(a^2-4)/(a^2-4a+4)-1/(a-2)/(a-1)/(a+2)
=[(a-2)(a+2)]/(a-2)^2-(a+2)/[(a-2)(a-1)]
=(a+2)/(a-2)-(a+2)/[(a-2)(a-1)]
=(a+2)/(a-2)*[1-1/(a-1)]
=(a+2)/(a-2)*[(a-1-1)/(a-1)]………………此处通分
=(a+2)/(a-2)*[(a-2)/(a-1)]
=(a+2)/(a-1)
=(1/2+2)/(1/2-1)
=-5
已知a2+2a-1=0,求(a-2/a2+2a - a-1/a2+4a+4)÷a-4/a+2的值
a²+2a-1=0
a²+2a=1
原式=[(a-2)/a(a+2)-(a-1)/(a+2)²]×(a+2)/(a-4)
={[(a-2)(a+2)-a(a-1)]/a(a+2)²}×(a+2)/(a-4)
=(a²-4-a²+a)(a+2)/[a(a-4)(a+2)²]
=(a-24)(a+2)/[a(a-4)(a+2)²]
=1/(a²+2a)
=1/1
=1
已知a^2 - 4a+1=0,求a^2 + 1/a^2 , a^4 + 1/a^4的值
a^2 - 4a+1=0
a^2+1= 4a
两侧同除以a得：
a+ 1/a=4
两边平方得：
a^2 +1/a^2 +2=16
a^2 +1/a^2 =16-2
a^2 +1/a^2 =14
a^2 +1/a^2 =14
两边平方得：
a^4 +1/a^4+2 =196
a^4 +1/a^4 =196-2
a^4 +1/a^4 =194
化简(1-a^2+8/a^2+4a+4)÷4a-4/a^2+2a
(1-a^2+8/a^2+4a+4)÷4a-4/a^2+2a
=(a²+4a+4-a²-8)/(a+2)²×a(a+2)/(4a-4)
=(4a-4)/(a+2)²×a(a+2)/(4a-4)
=a/(a+2)
计算：（1）/（2-a）-（（a+2）/（a²-2a）-（a-1）/（a²-4a+4））÷（a-4）/（2a）
原式=-1/(a-2)-[(a+2)/a(a-2)-(a-1)/(a-2)²]×2a/(a-4)
=-1/(a-2)-[(a+2)(a-2)-a(a-1)]/a(a-2)²×2a/(a-4)
=-1/(a-2)-(a²-4-a²+a)/a(a-2)²×2a/(a-4)
=-1/(a-2)-(a-4)/a(a-2)²×2a/(a-4)
=-1/(a-2)-2/(a-2)²
=-(a-2+2)/(a-2)²
=-a/(a-2)²
