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

Posted 15 days 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?

POSTED BY: C R
Answer
2 Replies

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.

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.)

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