With maxima 5.23.2:

(%i1) radcan((2*x^2/(x^2+1)-1)/sqrt(-4*x^2/(x^2+1)^2+1) );
(%o1)
1
radcan(((2*x^2-x^2-1)/(x^2+1))/sqrt((x^2-1)^2/(x^2+1)^2));

 
2
 
x  - 1
(%o2)
--------
                                                                                
        !
2    !
                                                                                
        !
x  - 1!
radcan(((x^2-1)*x/(x^2+1)^2-x/(x^2+1))/sqrt(-(x^2-1)^2/(x^2 +
1)^2 + 1) );
 
x
(%o3)
- ---------------
 
2
 
(x  + 1) abs(x)

same results

Thus, where reporting this bug?

On 27 jan, 22:41, kcrisman <kcris...@gmail.com> wrote:
> Hmm.
>
> Maxima 5.22.1http://maxima.sourceforge.net
> using Lisp ECL 10.4.1
> Distributed under the GNU Public License. See the file COPYING.
> Dedicated to the memory of William Schelter.
> The function bug_report() provides bug reporting information.
> (%i1) radcan((2*x^2/(x^2+1)-1)/sqrt(-4*x^2/(x^2+1)^2+1) );
> (%o1)                                  1
> (%i2) radcan(((2*x^2-x^2-1)/(x^2+1))/sqrt((x^2-1)^2/(x^2+1)^2));
>                                      2
>                                     x  - 1
> (%o2)                              --------
>                                    ! 2    !
>                                    !x  - 1!
> (%i3) radcan(((x^2-1)*x/(x^2+1)^2-x/(x^2+1))/sqrt(-(x^2-1)^2/(x^2 +
> 1)^2 + 1) );
>                                         x
> (%o3)                          - ---------------
>                                    2
>                                  (x  + 1) abs(x)
>
> I don't have access to a current Maxima, but if someone could check
> this out in 5.23.2 or whatever the latest is, that would be really
> great.  Then we'd have to file a bug report there.  Certainly the
> behavior should be similar for these.
>
> - kcrisman

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