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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 $p$?

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

A

$a-2{ p }^{ 2 }$

B

$\cfrac { { (p+2) }^{ 2 } }{ a }$

C

$\cfrac { { ({ p }^{ 2 }+2p+4) } }{ a }$

D

$\cfrac { { ({ 4p }^{ 2 }+p+4) } }{ a }$

E

$4a+4ap+a{ p }^{ 2 }$