Final answer:
The Least Common Denominator (LCD) of the rational expression 15/3(x + 7)(x - 7) is not applicable because there is only one fraction presented. However, the fraction can be simplified to 5/(x + 7)(x - 7), where the denominator itself is already in its least common form.
Step-by-step explanation:
The Least Common Denominator (LCD) of any set of rational expressions is the least common multiple (LCM) of their denominators. When we're looking at a single fraction like 15/3(x + 7)(x - 7), we really don't have multiple denominators to compare—there's just one denominator here. However, if we were comparing this fraction with another and were asked to find the LCD between them, we would look for the LCM of the different polynomial factors from each fraction's denominator.
The fraction 15/3(x + 7)(x - 7) itself can be simplified. First, divide the numeric part: 15 divided by 3 gives us 5. There are no common factors to reduce between the numerator and the polynomial factors in the denominator, so this fraction simplifies to 5/(x + 7)(x - 7). Hence, in the context of this single fraction, its simplified form is the most reduced version, and the denominator (x + 7)(x - 7) is already at its least common form.
If asked to find the LCD in conjunction with other fractions, you would list out all denominators, factor them completely if necessary, and find the LCM of all the factors involved. This LCM would then be the LCD for all the fractions being compared.