a=1/[2+√3]=(2-√3)/(2+√3)(2-√3)=2-√3
1/a=2+√3
a-1<0
于是
原式
=(a+1)(a-1)/(a-1)-√(a-1)²/[a(a-1)]
=(a+1)+(a-1)/[a(a-1)]
=a+1+1/a
=2-√3+1+(2+√3)
=3-√3+2+√3
=5