$$\begin{gathered} \text{if a,b,c are non-zero rational numbers then the sum of all the possible values of } \\ \frac{\left|a\right|}{a}+\frac{\left|b\right|}{b}+\frac{\left|c\right|}{c} \end{gathered}$$

$$\begin{gathered} \text{Let x=}\frac{\left|a\right|}{a}+\frac{\left|b\right|}{b}+\frac{\left|c\right|}{c} \\ If exactly one is negative then x=1, if two are negative then x=-1 \end{gathered}$$

$$\begin{gathered} if all three are negative x=-3, if all three are positive then x=3 \\ Then the required sum is 0 \end{gathered}$$