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In an English classroom, the teacher might explain a word to the students like this
You would use that at work or in your personal life.
When the word in question is explained in a book, which means the wording needs to be more formal, is the following wording clear and natural?
This word could be used at work and personal life.
There is no need to put a determiner before "personal life", right?
“This word could be used at work and personal life” doesn’t work, but it is not because of the lack of determiner. The problem is that “at” is not the correct preposition for “personal life.” If you were to change it to, “This word can be used at work and in personal life,” that works.
This word could be used at work and personal life.
This doesn't work. Even if the 'person' is non-specific, it is needed here. So either, "You could use this word.... your personal life" or "This word is useful both in business and private settings" or "This word works both at work and at home"... But plain 'work and personal life' doesn't work, because it tries to make a phrase 'work life', which is not a common phrase.
