答：
题目最后是tan6?没写全吧?是不是tan60°?
[2/(a+1)+(a+2)/(a²-1)]÷[a/(a+1)]
=[2(a-1)+(a+2)]/[(a+1)(a-1)]×(a+1)/a
=3a/[(a+1)(a-1)]×(a+1)/a
=3/(a-1)
a=(-1)^2012+tan60°=1+√3
所以3/(a-1)
=3/(1+√3-1)
=3/√3
=√3