Comment #3 on issue 2245 by matt...@gmail.com: assumption while canceling the polynomials
http://code.google.com/p/sympy/issues/detail?id=2245

This cases() function is a very nice idea. As to cancel(), this this a common design pattern to make a function do one thing at time. cancel() can be viewed as a fairly low-level function that only removes common factors using well established (and fast) algorithms, without going into any assumptions (in the most recent implementation it event doesn't care whether you use symbols or more complex expressions as the base for polynomials in the numerator and denominator). On top of this there should be more sophisticated functions, like cases(), implemented that take assumptions into account and use cancel() and other functions of similar kind as oracles.

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