I found this helpful from the U.S. Copyright site that Saucie provided, I know it's late but you know the saying...
Quote:
How much of someone else's work can I use without getting permission?
Under the fair use doctrine of the U.S. copyright statute, it is permissible to use limited portions of a work including quotes, for purposes such as commentary, criticism, news reporting, and scholarly reports. There are no legal rules permitting the use of a specific number of words, a certain number of musical notes, or percentage of a work. Whether a particular use qualifies as fair use depends on all the circumstances. See FL 102, Fair Use, and Circular 21, Reproductions of Copyrighted Works by Educators and Librarians
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This doesn't cover fan fiction but obviously discussing the books and using quotes, even rather lengthy quotes (Boro, I'm looking at you

) is in no way a violation of copyright. Accordingly I interpret this to also mean fan fiction is not a violation of copyright inasmuch as we give credit to Tolkien for the source which this site has adequately and satisfactorily given.