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Update: http://trac.sagemath.org/ticket/12737 has been merged in Sage - which still doesn't give you exactly what you want, but perhaps is more to your liking:

sage: ((1-x^2)/sqrt(1-2*x^2+x^4)).simplify_full()
-(x^2 - 1)/sqrt(x^4 - 2*x^2 + 1)