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Find the maximum of
$${1\over p} + {1\over q} + {1\over r}$$
where $p$, $q$ and $r$ are positive integers and
$${1\over p} + {1\over q} + {1\over r} < 1.$$
Prove that it is indeed a maximum.
Fracmax
Age 14 to 16
Challenge Level 
Find the maximum of
$${1\over p} + {1\over q} + {1\over r}$$
where $p$, $q$ and $r$ are positive integers and
$${1\over p} + {1\over q} + {1\over r} < 1.$$
Prove that it is indeed a maximum.
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