First we are going to find the common denominator of both fractions. To do that, we are going to multiply their denominators:

Now we can rewrite our expression using the common denominator:

Finally, we can use the trig identities:

and

to simplify our trig expression:
We can conclude that the correct answer is the fourth one.
Answer:
The roots of the function are x = -5/3 and 3. Select these.
Step-by-step explanation:
The roots of the function are the solutions to the function. They are also called the x-intercepts or zeros. To find them, factor the function completely and solve using the zero product property.
f(x) = (3x+5)(x2-6x+9)2 becomes f(x) = (3x+5)(x-3)^2
Set each factor equal to 0 and solve for x.
(3x+5)=0
3x = -5
x = -5/3
(x-3)^2 = 0
x - 3=0
x = 3