Q. Is there a rule I can point to in self-defense to justify the following hyphenation of compound nouns: “in private- and business life”? Business life is an unhyphenated compound noun in this sentence, but the first term, private, is hyphenated by virtue of being separated from the second term of its compound form, life. Does that sound right?

A. Not quite. Private life and business life are simply two adjective-noun combinations (not compounds), which you compacted a bit in your example by not repeating life. Think of similar constructions that you probably wouldn’t even consider hyphenating; yours is no different:

in big and small matters
through textbook and online instruction
at public and private venues