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For any three real numbers $a$, $b$, and $c$, with $b \neq c$, the operation $\P$ is defined by \[ \P(a, b, c) = \frac{a}{b-c}. \]What is $\P\left(\P(1,2,3), \P(2,3,1), \P(3,1,2)\right)$?

 Jul 6, 2018
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\(\text{For any three real numbers a, b, and c, with } b \neq c,\\\text{the operation P is defined by } P(a, b, c) = \frac{a}{b-c}.\\ \text{What is } P\left(P(1,2,3), P(2,3,1), P(3,1,2)\right)?\\ P(1,2,3)=\frac1{2-3}=-1\\ P(2,3,1)=\frac2{3-1}=1\\ P(3,1,2)=\frac3{1-2}=-3\\ P(-1,1,-3)=\frac{-1}{1-(-3)}=-\frac14\\ \text{I hope this helped,}\\ \text{Gavin.}\)

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 Jul 6, 2018

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