Functions $

Algebra Level 3

Let us define a binary operator, \($ \) such that

\[ $(a,b) = \begin{cases} \frac{ab-a+2}{2a} & , \quad & \text{ if } a+b \leq 3 \\ \frac{ab-b-2}{-2b} & , \quad & \text{ if } a+b > 3 \\ \end{cases} \]

Find \( $(2,1) + $(2,4) \).

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