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Well...
sage: Yt(x)=sqrt(-(x^2 - 1)^2/(x^2 + 1)^2 + 1)
sage: with assuming(x>0): Yt(x).canonicalize_radical()
2*x/(x^2 + 1)
whereas
sage: mathematica.FullSimplify(Yt(x),x>0).sage()
(2*x)/(x^2 + 1)
And, BTW :
sage: Yt(x).canonicalize_radical()
2*x/(x^2 + 1)
HTH,
