先化简,再求值:(a-1/a-a-2/a+1)÷2a^2-a/a^+2a+1,其中a满足a^2-a-1=0
问题描述：
先化简,再求值:(a-1/a-a-2/a+1)÷2a^2-a/a^+2a+1,其中a满足a^2-a-1=0
答
a^2-a-1=0
a²=a+1
原式=[(a-1)(a+1)/a(a+1)-a(a-2)/a(a+1)]×(a+1)²/a(2a-1)
=(a-1+a²+2a)/a(a+1)×(a+1)²/a(2a-1)
=(a+1)/a²
=(a+1)/(a+1)
=1