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