Any materials on fractional/quotient languages? In Hopcroft-Motwani-Ullman there are exercises on this topic. What is another good reference (textbook/website) for fractional/quotient regular languages, possibly with examples?
An Introduction to formal Languages and Automata 
Included in the University of Nottingham's Languages and Computation Course resources

The book An Introduction to Formal Languages and Automata  by Peter Linz can be used as an alternative or complement to Hopcroft-Motwani-Ullman.

An excerpt from

The latest edition of Linz’s theory textbook follows the same outline as the previous one: it begins with a chapter on mathematical preliminaries; moves through the Chomsky hierarchy (regular, context-free, and recursively enumerable languages, with a brief mention of context-sensitive languages); and concludes with one chapter each on the topics of undecidability, alternate models of computation, and complexity classes.


The presentation suits your needs : gives formal definitions, provide examples, give mathematical justifications (usually complete proofs), and end with a set of exercises. Solutions to some of the exercises appear in the appendix.


More than anything else, the book needs to provide readers with a broader framework that naturally motivates the many topics covered. Instructors looking for a general reference on automata and formal languages, or a textbook for a mathematically sophisticated audience, should take note that Linz’s book lacks a comprehensive bibliography (the one-page list of references consists primarily of other theory textbooks).


Overall, the work is appropriate for the author’s stated purpose: a textbook for an introductory undergraduate course on the theory of computation—provided that the students have sufficient mathematical preparation.