To simplify the expression 1/(9-4√5) + 1/(9+4√5), we first need to find a common denominator.

The common denominator is obtained by multiplying the two denominators together:

(9-4√5)(9+4√5) = 81 - 16(5) = 81 - 80 = 1

So, the expression becomes:

(1/(9-4√5)) + (1/(9+4√5)) = [(1(9+4√5) + 1(9-4√5))/((9-4√5)(9+4√5))] = [(9+4√5+9-4√5)/1] = (18/1) = 18

Therefore, 1/(9-4√5) + 1/(9+4√5) simplifies to 18.