Algebra

Well, let's first note something. 

We have $\frac{x}{x} = 1$ as long as x is not 0. 

We have $\frac{y}{y} = 1$ as long as y is not 0. 

We have $\frac{z}{z} =1$ as long as z is not 0. 

We finally have $\frac{xyz}{xyz} = 1$ as long as x,y,z are not 0. 

So, we have $1+1+1+1 = 4$ as long as $x,y,z \neq 0$

So there is only one possible value. 

Thanks! :)