"You can pick out the book you like."
Translation:Vous pouvez choisir le livre que vous aimez.
""tu aimes" has "tu", the subject pronoun, which does not elide in proper French and in writing."
Do you mean that in formal or written french, we must continue to write tu aimes? Why? Is it Because of the "u" in tu? Or is it because we must write vous instead of tu, as in "vous aimez".
Verbs that immediately follow other verbs are always* in the infinitive. We just don't always include the 'to' in English - if you translate this as 'are able to choose', the 'to' is still there. But that's the rule.
*As far as I know, at least. It's possible there's an exception. But if there is, it's not at this level of French :P
If you alternate "tu" and "vous" in the same sentence, it is inconsistent.
If you use "tu" with someone, "tu peux choisir le livre que tu aimes".
If you use "vous" with someone, "vous pouvez choisir le livre que vous aimez".
If you talk to 2 or more people, "vous pouvez choisir le livre que vous aimez".