Pattern matching for exactly one x

[Adam Povey]

Can anyone help me work out the regex for "one and only one x"?

Specifically, I have a question where I want to force students to simplify `(1 + x/sqrt(1+x^2)) / (x + sqrt(1+x^2))` but I haven't found something that will accept all of,

`(1+x^2)^(-1/2)`
`1/(1+x^2)^(1/2)`
`1/sqrt(1+x^2)`

Sorry,

Adam

[Christian Lawson-Perfect]

That's a tricky one! I assume you'd also accept `sqrt(1+x^2)^-1`, but you don't like `sqrt(1+x^2)/(1+x^2)`, which is what you get by 'rationalising the denominator'? 

I'd be inclined to prompt the student with something like "write your answer in the form "1/sqrt(f(x))", and just ask for the "f(x)". Otherwise, explaining what you will and won't accept will be very difficult, never mind working out how to get the pattern matcher to do it for you.

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