Final Answer:
The expression ((f)/(g))(x) is equal to (2(2x + 3))/(2x + 5).
Step-by-step explanation:
Begin by writing out the expressions for f(x) and g(x):
f(x) = 4x^2 + 6x
g(x) = 2x^2 + 13x + 15
Set up the expression for ((f)/(g))(x):
(f/g)(x) = (4x^2 + 6x) / (2x^2 + 13x + 15)
Factor the numerators and denominators:
(2x(2x + 3)) / ((2x + 5)(x + 3))
Cancel out common factors:
(2(2x + 3)) / (2x + 5)
Simplify the expression:
(2(2x + 3)) / (2x + 5)
Therefore, ((f)/(g))(x) simplifies to (2(2x + 3))/(2x + 5).