Question

先化简，再求值：[（a的平方-4/a的平方-4a+4)-(1/2-a)]/(2/a的平方-2a)

Answer 1

[(a^2-4)\(a^2-4a+4)-1/(2-a)]÷2/(a^2-2a)
=[(a+2)(a-2)/(a-2)^2+1/(a-2)])÷2/[a(a-2)]
=(a+3)/(a-2)*[a(a-2)]/2
=a(a+3)/2
因为
x^2+3x+1=0
x(x+3)=-1
又a是方程x^2+3x+1=0的根
所以a(a+3)=-1
则原式=a(a+3)/2=-1/2

Answer 2

等与负二分之一

Answer 3

[（a的平方-4)/(a的平方-4a+4)-1/(2-a)] ÷2/（a的平方-2a)
[(a+2)(a-2)/(a-2)(a-2)+1/(a-2)]*a*(a-2)/2
=[(a+2)/(a-2)+1/(a-2)]*a*(a-2)/2
=[a+3]*a/2
=a*a/2+3a/2