1/a+1/b=1
(a+b) =ab
a(b-1) =b
a= b/(b-1)
S = (2+b)/(2ab)
= (2+b)(b-1)/( 2b^2)
S' = [2b^2(2b+1) - 4b(b^2+b-2)] /(4b^4)
S' =0
b(2b+1)-2(b^2+b-2) =0
-b+4=0
b=4
S''(4) a=4/3
max S = (2+4)/(2(4/3)4) = 9/16
1/a+1/b=1
(a+b) =ab
a(b-1) =b
a= b/(b-1)
S = (2+b)/(2ab)
= (2+b)(b-1)/( 2b^2)
S' = [2b^2(2b+1) - 4b(b^2+b-2)] /(4b^4)
S' =0
b(2b+1)-2(b^2+b-2) =0
-b+4=0
b=4
S''(4) a=4/3
max S = (2+4)/(2(4/3)4) = 9/16