原式=[(a+1)(a-1)+2]/(a+1)×1/(a²+1)
=(a²-1+2)/(a+1)×1/(a²+1)
=(a²+1)/(a+1)×1/(a²+1)
=1/(a+1)
=1/(根号2-1+1)
=1/根号2
=根号2/2