Incorrect reduction

Questions
1

Is there an incorrect theorem embedded in wolfram alpha, or is this a bug? See image.

Any time I enter " (i (2 x^* - 1))/(2 (x^* - 1) x^* ) " it reduces to "i / x^* " I need to show an equivalence, but when this is on the right hand side of the equation, it reduces to this " i/x^* " nonsense. Any ideas? I see why it’s doing it (order of operations), but it’s wrong.

problem.jpg
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2

Here’s an example…

example.jpg
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3

Incorrect reduction

4

Common factors are cancelled (standard in rational function fields). Think of it as a removable singularity, one that, well, got removed.

5

(2 (5 - I 7) - 1) is not the same as 2 ((5 - I 7) - 1)

6

Daniel, you might want to look at this again. Look at my numerical example I provided. Then go ahead and enter the same calculation using just x instead of the complex conjugate of x. It won’t cancel in either of these, for the same reason it shouldn’t for the former. It’s inconsistent.

7

Ah, yes. Bad precedence. I filed a bug report for this.

8

Thanks, and here’s a visual just in case.

nosolutionsexist.jpg
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9

And Gustavo is right’o! But not exactly as I entered it.

10

Okay, weird…just narrowed it down. In my first image I didn’t include the equation as I entered it. It’s a bug in how it’s reading my input. Take a look at this image now, as it includes what I actually type.

enteringinput.jpg
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11

The temporary work around is to put additional parenthesis around the 2 x^* in the numerator.

12

I am confused. What is x^* ?

13

X^* means complex conjugate of X.

14

I understand now.

X^* is interpreted as the complex conjugate in natural language, but it is a syntax error in Mathematica.

15

Yep. Seems that way.