Final answer:
To find the LCD for the given rational expressions, you have to multiply the binomial denominators (2x + 16) and (3x - 27) as they have no common factors, making the LCD (2x + 16)(3x - 27).
Step-by-step explanation:
To find the least common denominator (LCD) for the set of rational expressions x/2x + 16 and -4x/3x - 27, you need to identify the least common multiple (LCM) of the denominators. As the question appears to have typos, let's assume the expressions are in their simplest form:
First expression: x/(2x + 16)
Second expression: -4x/(3x - 27)
We need to find the LCM of (2x + 16) and (3x - 27). These two expressions are binomials and do not share any common factors, so the LCM is simply their product.
The LCD is therefore (2x + 16)(3x - 27).