1/(1+x) + 1/(1 + 1/x) = 1/(1+x) + x/(x+1) = (1+x)/(1+x)=1
x=a^n (is a red herring)
What do you mean a red herring, all you did was rename the variable, if the whole thing was 1, it's obvious that it CANNOT depend on a or n by definition of being a constant.
(red herring) There was no reason to put it in the form a^n, a simple x will do.
I disagree, if it were put in the other form it would be just what it is, the fact that they used
means they probably wanted to get the student practice at seeing the more general principles in more specific situations, which is arguably as important as being able to see the more general principles. For example, of course you can say:
" and people will think "quadratic formula"
However, saying "Solve
" is perhaps a more reasonable question to get in some applications, and indeed it is just a disguised quadratic, but what use is the formula to you if you cannot see the general in the specific, something which may be one of the most central ideas in mathematics as a subject. It's the reason we can tell that some students just see math as a bunch of symbol pushing and cannot solve problems once they've just been even slightly
tweaked to be in different forms which are still essentially the same as the more obvious versions.