In fact, the rational number are rational because they are a fractions of two numbers. it may be different with positive integers or the sum of egyptians fractions which are link by a rule.

$1/2 = 1/3 + 1/6$

$1/3 = 1/4 + 1/12$

$1/4 = 1/5 + 1/20$

$1/5 = 1/6 + 1/30$

$1/6 = 1/7 + 1/42$

so we can say  $1/U(1)=1/U(0)-1/U(0)U(1)$

$U(1)/U(0)-U(1)/U(0)U(1)=1  $ if $ U(1)=U(0)+1$

it is in french, but you can study the egyptian fraction (and the code) in clouds: 
http://jeux-et-mathematiques.davalan.org/arit/egy/index.html#table2

There are the same question here.
http://math.stackexchange.com/questions/238496/a-question-about-rational/238511#238511