Question 1033415
{{{x/abs(x)+y/abs(y)+z/abs(z)+(xyz)/abs(xyz)}}}
<pre>
Case 1. All three variables positive:  x>0, y>0, z>0

{{{x/x+y/y+z/z+(xyz)/(xyz)}}}

{{{1+1+1+1}}}{{{""=""}}}{{{4}}}

Case 2. Two of the variables positive, one negative
By symmetry, it doesn't matter which one is negative,
the answer will be the same.  Say, only y is negative:

x>0, y<0, z>0

{{{x/x+y/(-y)+z/z+(xyz)/(x(-y)z)}}}

{{{1-1+1-1)}}}{{{""=""}}}{{{0}}}

Case 3. One of the variables positive, two negative
Also by symmetry, it doesn't matter which one is positive,
the answer will be the same.  Say, only x is positive 

x>0, y<0, z<0

{{{x/x+y/(-y)+z/(-z)+(x(-y)(-z))/(x(-y)(-z))}}}

{{{1-1-1+1)}}}{{{""=""}}}{{{0}}}

Case 4. All three negative:  x<0, y<0, z<0

{{{x/(-x)+y/(-y)+z/(-z)+(xyz)/((-x)(-y)(-z))}}}

{{{-1-1-1-1}}}{{{""=""}}}{{{-4}}}

In increasing order, separated by commas:

-4,0,4

Edwin</pre>