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# Operation

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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(P(1,2,3),P(2,3,1),P(3,1,2))?

Apr 6, 2021

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$P(1,2,3)=\frac{1}{2+3}=\frac{1}{5}$

$P(2,3,1)=\frac{2}{3+1}=\frac{2}{4}=\frac{1}{2}$

$P(3,1,2)=\frac{3}{1+2}=\frac{3}{3}=1$

$P(\frac{1}{5},\frac{1}{2},1)=\frac{\frac{1}{5}}{\frac{1}{2}+1}=\frac{1}{\frac{15}{2}}=\boxed{\frac{2}{15}}$

Apr 6, 2021