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This question already has an answer here:

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?

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marked as duplicate by m_goldberg, bbgodfrey, jkuczm, mikado, J. M. will be back soon Jul 30 '17 at 15:28

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ Note that entering x ^ 2 == x ^ 2 / x directly automagically performs the cancellation. In any event, read up on the case of "generically correct" solutions. $\endgroup$ – J. M. will be back soon Jul 30 '17 at 8:23
  • $\begingroup$ The answer Reduce gave you is entirely correct. The quadratic form` x(x - 1)` has roots at 0 and1. $\endgroup$ – m_goldberg Jul 30 '17 at 8:50
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    $\begingroup$ I'm voting to close this question as off-topic because the issued raised is not really a problem; it is arises from the OP's misunderstanding of the result returned by Mathematica. $\endgroup$ – m_goldberg Jul 30 '17 at 8:51
  • $\begingroup$ You could use my RestrictDomain function: Reduce[RestrictDomain[x^2 == x^2/x, x, Complexes], x] (* x == 1 *). $\endgroup$ – jkuczm Jul 30 '17 at 12:47