化简a^2-2a+1/a^2-1+a^2-a/a+1+2/a,其中a=根号3
问题描述：
化简a^2-2a+1/a^2-1+a^2-a/a+1+2/a,其中a=根号3
答
原式=(a-1)^2/(a+1)(a-1)+a(a-1)/(a+1)+2/a
=(a-1)/(a+1)+a(a-1)/(a+1)+2/a
=(a+a^2-a)/(a-1)+2/a
=a^2/(a-1)+2/a
=(a^3+2a-2)/a(a-1)
=(a^3+2a-2)/(a^2-a)
=(3√3+2√3-2)/(3-√3)
=(5√3-2)/(3-√3)
=(15√3+15-6-2√3)/(9-3)
=(9+13√3)/6