eq. 1: f(x) = 4x / 4(1-x) + 4x
replace x with 1-x, we get
eq 2: f(1- x) = 4(1-x) / 4(1-x) + 4x
add eq 1 and eq 2
f(x) + f(1-x) = [ 4x + 4(1-x) ] / [ 4(1-x) + 4x ]
f(x) + f(1-x) = 1
x = 1/65
f(1/65) + f(64/65) = 1
f(2/65) + f(63/65) = 1
f(3/65) + f(62/65) = 1
f(4/65) + f(61/65) = 1
f(5/65) + f(60/65) = 1
.
.
.
f(30/65) + f(35/65) = 1
f(31/65) + f(34/65) = 1
f(32/65) + f(33/65) = 1
on summing all we get
f(1/65) + f(2/65) + f(3/65) + ...................................................................... + f(64/65) = 32
so answer is 32