Final answer:
The least common denominator of the expressions (x+1), (x+1), and (5+2x) is (x+1)(5+2x) or (x+1)(2x+5), as these expressions represent the product of the distinct factors present in the denominators.
Step-by-step explanation:
To find the least common denominator (LCD) of the given expressions (x+1), (x+1), and (5+2x), we need to look for the smallest expression that can be divided by all three denominators without leaving a remainder. Since the expressions (x+1) and (5+2x) are unlike and neither is a multiple of the other, we multiply them together to get the LCD.
The correct option is therefore (x+1)(5+2x) or (x+1)(2x+5), which are equivalent because multiplication is commutative. This means option a and option b are both correct answers as they are equivalent expressions, having just switched the order of the binomials. Option c and d are incorrect because they do not account for both unique factors in the denominators.