Question 1209357
**1. Consider the Sign Combinations**

* **All positive:** If x, y, and z are all positive, then:
    (x + y + z) / (|x| + |y| + |z|) = (x + y + z) / (x + y + z) = 1

* **All negative:** If x, y, and z are all negative, then:
    (x + y + z) / (|x| + |y| + |z|) = -(x + y + z) / (-(x + y + z)) = 1

* **Two positive, one negative:** 
    * Let's say x and y are positive, and z is negative:
        (x + y + z) / (|x| + |y| + |z|) = (x + y - |z|) / (x + y + |z|) 
        This value will be between 0 and 1, depending on the relative magnitudes of x, y, and z.

* **Two negative, one positive:** 
    * Similar to the previous case, the value will be between -1 and 0.

* **One positive, two negative:** 
    * Similar to the previous cases, the value will be between -1 and 0.

**2. Determine the Possible Values**

* Based on the sign combinations, the possible values of (x + y + z) / (|x| + |y| + |z|) range from **-1 to 1**, inclusive.

**Therefore, the possible values of (x + y + z) / (|x| + |y| + |z|) are all real numbers in the interval [-1, 1].**