Question

化简求值；{[(a-2)/(a^2+2a)]-[(a-1)/(a^2+4a+4)]}除以(a-4)/(a+2),其中a满足a^2+2a-1=0

应该能看懂吧

Answer 1

{[(a-2)/(a^2+2a)]-[(a-1)/(a^2+4a+4)]}除以(a-4)/(a+2)
={[(a-2)/a(a+2)]-[(a-1)/(a+2)²]}除以(a-4)/(a+2)
=[(a+2)(a-2)-a(a-1)]/a(a+2)²×(a+2)/(a-4)
=1/(a²+2a)
=1

追问

a的值是多少，关键是求值

追答

a^2+2a-1=0

a^2+2a=1

{[(a-2)/(a^2+2a)]-[(a-1)/(a^2+4a+4)]}除以(a-4)/(a+2)
={[(a-2)/a(a+2)]-[(a-1)/(a+2)²]}除以(a-4)/(a+2)
=[(a+2)(a-2)-a(a-1)]/a(a+2)²×(a+2)/(a-4)
=1/(a²+2a)
=1/1
=1

不用求出a的值,求出a²+2a=1,化简后代入就可以了