Difficult# Solving Rational Equations

ACTMAT-WVRKSV

For the equation below, $a$, $p$ and $q$ are non-zero real numbers.

Which of the following represents the value of $q$, in terms of $a$ and $p$?

$$ \frac { a }{ 2 } =\frac { 2p+2 }{ q } +\frac { { p }^{ 2 } }{ 2q } $$