1/(7+4*sqrt(3))+ 1/(7-4*sqrt(3))

1/(7+4*sqrt(3))+ 1/(7-4*sqrt(3))   getting a common denominator, we have

[(7 - 4√3)  + (7 + 4√3)] / [ 49  - 16(3)] = 

14 / (49 - 48) =

14 / 1

14

Answer is 14.

you can aply (a+b)(a-b)=a^2-b^2 this formula on this math problem.