What is the reciprocal of the sum of the reciprocals of 6 and 8 and how did solve?

The sum of the reciprocals of 6 and 8 equals to 7/24.

1/6 + 1/8 (multiply by 4/4 the first fraction, multiply by 3/3 the second fraction, since their common denominator is 24)
= 1x4/6x4 + 1x3/8x3
= 4/24 + 3/24
= 7/24

Thus, the reciprocal of 7/24 is 24/7.