this will not simplify to 1, but it is 1



(%i1) ratsimp(( (signum(x - 1) + 1) * signum(x + 1) - signum(x - 1)));
(out1)                                       (signum(x - 1) + 1) signum(x + 1) - signum(x - 1)

(%i3) radcan( (signum(x - 1) + 1) * signum(x + 1) - signum(x - 1));
(out2)                                       (signum(x - 1) + 1) signum(x + 1) - signum(x - 1)

(%i4) factor( (signum(x - 1) + 1) * signum(x + 1) - signum(x - 1));
(out4)                                  signum(x - 1) signum(x + 1) + signum(x + 1) - signum(x - 1)

(%i5) expand( (signum(x - 1) + 1) * signum(x + 1) - signum(x - 1));
(out5)                                  signum(x - 1) signum(x + 1) + signum(x + 1) - signum(x - 1)