Question

化简求值a²-1/a²+2a+1+2a-a/a-2÷a 其中a=根号2+1

Answer 1

原式=(a+1)(a-1)/(a+1)^2+(a)/(a-1)*1/a
=(a-1)/(a+1)+1/(a-1)
=[(a-1)^2+1]/(a^2-1)
=[(根号2)^2+1]/(2+1+2根号2-1)
=3/(2+2根号2)
=3(根号2-1)/2(2-1)
=3(根号2-1)/2