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 $pqr - \frac1{pqr}$ .