To simplify the expression, we will first expand the numerator:

(b+2)^2 = b^2 + 4b + 4
(b-2)^2 = b^2 - 4b + 4

Now, multiply these two together:

(b^2 + 4b + 4)(b^2 - 4b + 4)
= b^4 - 4b^2 + 4b^2 - 16b^2 + 16b + 16b + 16
= b^4 - 16b^2 + 32b + 16

Therefore, the expression simplifies to:

(b^4 - 16b^2 + 32b + 16) / 32b
= (b^4 - 16b^2 + 32b + 16) / (32b)