Final answer:
The least common denominator (LCD) of the given rational expressions is (7x + 1)(7x - 1)(x - 2)(x + 2).
Step-by-step explanation:
The least common denominator (LCD) of rational expressions is the smallest common multiple of the denominators of the expressions. To find the LCD of the given rational expressions (A), (B), (C), and (D), we need to identify the unique factors present in each expression and include them in the LCD.
Factoring each expression, we have:
(A) = (7x + 1)(x - 2)(x + 2)
(B) = (7x - 1)(x - 2)(x + 2)
(C) = (7x + 1)(x - 2)
(D) = (7x + 1)(7x - 1)(x - 2)(x + 2)
The LCD will be the product of all the unique factors present in the expressions. In this case, the unique factors are (7x + 1), (7x - 1), (x - 2), and (x + 2).
Therefore, the LCD is (7x + 1)(7x - 1)(x - 2)(x + 2).