How do I tell her, without offending her, that I don't want non-students in class. I don't want to lose her as a friend/student, and she didn't take the hint when I suggested her friend would be okay.
Sadly, this isn't the first time this has happened. It is the third, and it's been three different people. I don't understand the presumption of people, but mostly I don't know how to handle it.
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Friend? She is no friend. She has offended you multiple times by attending without paying. The only occasion when someone other than a student should attend a class is if the student needs an interpreter. It appears you set a precedent by allowing her to attend the three previous times. This will probably continue unless you take a stand. It is not fair to your other paying students.