Let [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] be positive real numbers with [unparseable or potentially dangerous latex formula] Let [unparseable or potentially dangerous latex formula] be the maximum possible value of [unparseable or potentially dangerous latex formula] for which the system of equations
[unparseable or potentially dangerous latex formula]
has a solution [unparseable or potentially dangerous latex formula] satisfying [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] Then [unparseable or potentially dangerous latex formula] can be expressed as a fraction [unparseable or potentially dangerous latex formula] where [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] are relatively prime positive integers. Find [unparseable or potentially dangerous latex formula]