For the Following Figure, Express the Length AB as a Function

Multiple Choice

For the following figure, express the length AB as a function of x. (Hint: Note the similar triangles.)

A) $A B ( x ) = \frac { ( x + 2 ) \sqrt { x ^ { 2 } + 9 } } { x ^ { 2 } }$
B) $A B ( x ) = \frac { ( x + 2 ) \sqrt { x ^ { 2 } + 9 } } { x }$
C) $A B ( x ) = \frac { ( x + 3 ) \sqrt { x + 4 } } { x }$
D) $A B ( x ) = \frac { ( x + 3 ) ^ { 2 } ( x + 2 ) } { x }$
E) $A B ( x ) = \frac { ( x + 3 ) \left( x ^ { 2 } + 2 \right) } { x }$