原式=(a+2)²/(a+1)÷[(a-1)(a+1)-3]/(a+1)
=(a+2)²/(a+1)÷(a²-4)/(a+1)
=(a+2)²/(a+1)×(a+1)/(a+2)(a-2)
=(a+2)/(a-2)
=(2+√3+2)/(2+√3-2)
=(4+√3)/√3
=(4√3+3)/3