For example, if you enter
Reduce [x ^ 2 == x ^ 2 / x, x]
The output is
x == 0 || x == 1
Well, the correct answer is x == 1. Although this is a trivial example, is there no possibility that similar errors will occur in the process of internal calculation?
x ^ 2 == x ^ 2 / xdirectly automagically performs the cancellation. In any event, read up on the case of "generically correct" solutions. – J. M.'s missing motivation Jul 30 '17 at 08:23Reducegave you is entirely correct. The quadratic formx(x - 1)has roots at 0 and1. – m_goldberg Jul 30 '17 at 08:50RestrictDomainfunction:Reduce[RestrictDomain[x^2 == x^2/x, x, Complexes], x] (* x == 1 *). – jkuczm Jul 30 '17 at 12:47