AMC10 2005 10A, Problem 2

For each pair of real numbers $a \neq b$, define the operation $\star$ as $(a \star b) = \frac{a+b}{a-b}$. What is the value of $((1 \star 2) \star 3)$?

Solution: $((1 \star 2) \star 3) = \left(\left(\frac{1+2}{1-2}\right) \star 3\right) = (-3 \star 3) = \frac{-3+3}{-3-3} = 0 \Longrightarrow \fbox{0}$

Answer: 0