2/（a-1）+（a²-4a+4）/（a²-1）÷（a-2）/（a+1）.
=2/(a-1)+(a-2)²/(a+1)(a-1)×(a+1)/(a-2)
=2/(a-1)+(a-2)/(a-1)
=a/(a-1)
当a=1+√2时
原式=(1+√2)/√2
=(2+√2)/2