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What is the least common denominator of ( x+1 ), ( x+1 ), and ( 5+2x )?

a. ( (x+1)(5+2x) )
b. ( (x+1)(2x+5) )
c. ( (2x+5) )
d. ( (x+1) )

User Lavakush
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1 Answer

4 votes

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.

User Jady
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