That is indeed strange. And why restrict it to rationals, when it's true for every real (or every complex, whatever)? It's even true for integers, under a suitable interpretation of what is meant by dividing by 2 in that case.

It's also totally trivial when you rewrite it slightly: (r + r + 1 - 1) / 2. So basically adding r to itself to get 2r then dividing by 2 gives you back r, with a pointless plus and minus 1 thrown in.

It's trivial only if you are simplifying mathematical expression.

When you have to go the opposite direction, you start with r and must turn it something that fits some other expression, there are infinite ways to proceed. Right ones rarely just pop up into your mind.

Remembering trivial identities things like that are useful as small intermediate steps when manipulating expressions.

But this still does not answer why this expression is specifically listed for rational numbers as it is true for subsets of the rational numbers like the integers as well as for supersets of the rational numbers like the real numbers.