# WA says '7x/x = 7' only if x ≠ 0, but has no problem with 'ax/x = a'. Why?

Posted 7 months ago
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 In WA, entering 'ax/x = a' will return 'True.'If 'a' is replaced with a constant, it changes its rule. '7x/x = 7' will say that it's true as long as x ≠ 0.Why is it that 'ax/x = a' is true until 'a' is replaced with a constant? Answer
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Posted 7 months ago
 Mathematica was originally designed so that expressions such as a x/x are simplified to just a before any other mechanism or check could intervene. This is probably efficient for calculations, but it exposes the system to criticism. I suppose that Wolfram Alpha has new code that catches the problem, but only when the coefficient is numerical. Answer
Posted 6 months ago
 Interestingly, in Mathematica (version 11.3) itself:  (7 x)/x == 7 (* True *) (a x)/x == a (* True *) Reduce[(7 x)/x == 7, x] (* True *) Reduce[(a x)/x == a, x] (* True *) (Simplify applied to each equation also yields True as output.) Answer
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