Find the least common denominator for the expression.
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A) (3x + 2)(2x + 3)
C) (3x + 2)(2x + 3)(x + 1)

Question

Find the least common denominator for the expression.
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A) (3x + 2)(2x + 3) 
C) (3x + 2)(2x + 3)(x + 1)

Quizplus · Accepted Answer

The expression does not have any common factors, so we cannot simplify before finding the LCD. The factors of the denominators are (3x+2), (2x+3), and (x+1). Therefore, the least common denominator is the product of these factors: (3x+2)(2x+3)(x+1). This matches choice C. To find the least common denominator, we need to factor each denominator into its prime factors and then take the union of all the prime factors, taking the highest power of each. In this case, the denominators are (3x+2)(2x+3), (3x+2)(2x+3)(x+1), and (x+1). Factoring each, we get (3x+2)(2x+3), (3x+2)(2x+3)(x+1), and (x+1). Taking the union of all the prime factors and highest powers, we get (3x+2)(2x+3)(x+1), which is choice C.

Find the Least Common Denominator for the Expression