Final answer:
The least common denominator (LCD) for the rational expressions 3/x^2 and 8/3x is 3x^2.
Therefore, the correct answer is a) 3x^2.
Step-by-step explanation:
To find the least common denominator (LCD) for the two rational expressions 3/x^2 and 8/3x, we need to consider the different variables and their powers in the denominators.
The first denominator x^2 is the square of x, while the second denominator 3x includes both a 3 and the first power of x.
The least common denominator is found by multiplying each distinct factor by the highest power that factor has in any of the denominators.
The LCD will be the product of the highest powers of both 3 and x seen in any single denominator, which is 3x^2.