Final answer:
The least common denominator (LCD) for the fractions 3/2, x/(2x+1), and x/(2x-8) is the product of their denominators, which is 2 * (2x+1) * (2x-8).
Step-by-step explanation:
To find the least common denominator (LCD) for the set of rational expressions (3/2), (x/(2x+1)), (x/(2x-8)), we must identify a common denominator that each expression's denominator can divide into without leaving a remainder. This usually involves factoring each denominator and then finding a product that includes each factor at least as many times as it occurs in any of the denominators.
The first fraction already has a simple denominator of 2, which will likely be a part of our LCD. The second and third fractions have more complicated denominators that can't be factored further, so we have no common factors between them. Therefore, the LCD is simply the product of all three denominators: 2 * (2x+1) * (2x-8).