先化简,再求值:1-(a-1/a)÷（a²+2a+1）/a
问题描述：
先化简,再求值:1-(a-1/a)÷（a²+2a+1）/a
答
1-(a-1/a)÷（a²+2a+1）/a
=1-(a²-1)/a * a/(a+1)²
=1-(a-1)(a+1)/(a+1)²
=1-(a-1)/(a+1)
=(a+1-a+1)/(a+1)
=2/(a+1)a=根号3-1原式=2/(√3-1)=2(√3+1)/[(√3-1)(√3+1)]=2(√3+1)/2=√3+1