Let x, y, and z be nonzero real numbers

x/|x|   = + or - 1   the same with the y and z terms

+-1  +-1  +-1  =   3,-3, 1, -1

Let x, y, and z be nonzero real numbers. Find all possible values of x/|x| + y/|y| + z/|z|.

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\(If\ x\{y,z\}<0\ than\ \frac{x\{y.z\}}{|x\{y,z\}|}=-1\\ If\ x>0\ than\ \frac{x}{|x|}=1\)

\(\frac{x}{|x|}+\frac{y}{|y|}+\frac{z}{|z|}=\)

1+1+1                = 3

1+1(-1)              = 1

1+(-1)+1            = 1

1+(-1)+(-1)        = -1

-1+1+1              = 1

-1+1+(-1)          = -1

-1+(-1)+1          = -1

-1,+(-1)+(-1)     = -3

\(\frac{x}{|x|}+\frac{y}{|y|}+\frac{z}{|z|} \in \{ -3,-1,\ 1,\ 3\}\)

  !