Final answer:
To simplify the expression, common factors (x + 2) and x are canceled out after multiplying the numerators and denominators together, resulting in the simplest form 2 / (3y).
Step-by-step explanation:
To simplify the expression (2x + 4) / (3xy) * (x / (x + 2)), we need to multiply the numerators together and the denominators together, simplifying by common factors as needed. First, we factor the numerator of the first fraction:
2x + 4 = 2(x + 2)
This allows us to see that there is a common factor of (x + 2) in the numerator of the first fraction and the denominator of the second fraction. So, the expression becomes:
2(x + 2) / (3xy) * (x / (x + 2)) = 2x / (3xy)
Now we can cancel out the common factor of x:
2x / (3xy) = 2 / (3y)
Therefore, the simplified expression is 2 / (3y), which corresponds to option (a).