Numbers and Reciprocals

Algebra Level 4

Three positive real numbers \(p,q,r\) satisfy

\[ \begin{eqnarray} \frac { 1 }{ p } +q &=& 2\\ \frac { 1 }{ q } +r &=& 3\\ \frac { 1 }{ r } +p &=& 5\\ \end{eqnarray} \]

Find the sum of all possible values of \(p\).

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