Hi Janet, this a peculiar bug you have found and we're looking into it now.

You can see the steps by avoiding the period in your query, i.e. Solve ((5)/(p-2))-((7)/(p+2))=((12)/(p^2-4)): http://www.wolframalpha.com/input/?i=Solve+((5)/(p-2))-((7)/(p%2B2))=((12)/(p^2-4))

You have the ability to see step from Wolfram|Alpha and Mathematica, but accessing them through Wolfram|Alpha is encouraged because hints are only available this way.

Dear Janet,

it seems to be doing exactly what you are paying for. You probably speak about Wolfram Alpha not Mathematica, I assume. Copying your equation in and hitting enter, you get to a window where you can click on "show steps". This gives you:

It is not quite clear what went wrong when you did it. Anyway, it works just fine.

Cheers, Marco