# Manipulating Reciprocals

Algebra Level 4

$$p$$, $$q$$, and $$r$$ are all positive numbers, and they all satisfy the following equations: $$p - \frac1q = 3$$, $$q - \frac1r = 4$$, $$r - \frac1p = 5$$. Compute the value of $$pqr - \frac1{pqr}$$.

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