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Suppose $a, b$, and $c$ are nonzero real numbers, and $a+b+c=0$. What are the possible value(s) for $\frac{a}{\textbar a\textbar}+\frac{b}{\textbar b\textbar}+\frac{c}{\textbar c\textbar}+\frac{a b c}{\textbar a b c\textbar} ?$ (2017 AMC 8 Problem, Question \#21) 
Overseas Competition->Knowledge Point->Combinatorics->Mathematical Thoughts->Absolute Value
There are 2 cases to consider:  \textbf{Case 1:} 2 of $a, b$, and $c$ are positive and the other is negative. WLOG, we can assume that $a$ and $b$ are positive and $c$ is negative. In this case, we have that $$ \frac{a}{\textbar a\textbar}+\frac{b}{\textbar b\textbar}+\frac{c}{\textbar c\textbar}+\frac{a b c}{\textbar a b c\textbar}=1+1-1-1=0 \text {. } $$  \textbf{Case 2}: 2 of $a, b$, and $c$ are negative and the other is positive. Without loss of generality, we can assume that $a$ and $b$ are negative and $c$ is positive. In this case, we have that $$ \frac{a}{\textbar a\textbar}+\frac{b}{\textbar b\textbar}+\frac{c}{\textbar c\textbar}+\frac{a b c}{\textbar a b c\textbar}=-1-1+1+1=0 \text {. } $$  Note these are the only valid cases, for neither 3 negatives nor 3 positives would work, as they cannot sum up to 0 . In both cases, we get that the given expression equals $(\mathbf{A}) 0$. 