Mathematics

Mathematics

Problem

AMC 8,2001 Problem 12: If a⊗b=a+ba−ba \otimes b = \frac{a+b}{a-b}, then (6⊗4)⊗3=(6 \otimes 4) \otimes 3 =
Intuitive explanation

This problem is about applying a custom operation twice in sequence. The key insight is to treat the operation like any function: compute the inner operation first to get a single number, then use that result as the first input to the outer operation. Don't let the unfamiliar symbol ⊗\otimes intimidate you—just substitute carefully into the definition each time.

Intuitive explanation

This problem is about applying a custom operation twice in sequence. The key insight is to treat the operation like any function: compute the inner operation first to get a single number, then use that result as the first input to the outer operation. Don't let the unfamiliar symbol ⊗\otimes intimidate you—just substitute carefully into the definition each time.

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