Is this a valid expression? x/x-1 = 1/x-1 It would appear that x=1 but that would...

[JeffM]

What I like to encourage is, after solving one way, to look for others, which stops students from falling into ruts, and keeps them flexible.

That is an interesting thought. Next time I have a strong student, I shall keep it in mind.

Sadly, by the time I usually get someone to tutor, he or she has been thoroughly convinced that math is a mess of formulas and techniques to memorize without understanding. So I tend to focus on one thing at a time. Let them master one technique and build confidence that they understand why it works and can do it without too many errors.

 

[dogleg]

I'm not sure there's any difference of opinion. After all, I did start by suggesting substitution, at least as a fallback (though I didn't actually do it, so I missed the fact that the quadratic formula is never needed).

What I like to encourage is, after solving one way, to look for others, which stops students from falling into ruts, and keeps them flexible. In this case, the oddity of the question about xy led me to look in other directions first. And, not knowing the context, perhaps this was a contest-type problem in which that is the point. But I don't think it was. In fact, the real problem may have been worded as "what can x and y be?"

Thanks for your comments and suggested alternatives. A group of us meet for coffee almost every week; all of us have been retired for quite a while . Some of us were engineers,some high school and community college math teachers etc. who are rusty as the devil in math and a lot of these questions come from grand kids who think we all should still be sharp in math..WRONG! Wait for your turn. Anyway if it is OK I am sure there will be plenty more problems to solve. Again, thanks to all you smart 'young' people.