Question

What is the common denominator of (2)(3x-2), (2-4)(5), and (22x+7)(x²-4x+20) in the complex tion ((x + 2)(x - 2))(x²)?

a) 3x - 2

b) 5(x + 2)(x - 2)

c) x² - 4x + 20

d) x²(x + 2)(x - 2)

Answer 1

The common denominator is (x + 2)(x - 2)x², as it is the only option that includes all the factors from the given complex fraction and other expressions without repetition.

Step-by-step explanation:

The question is asking for the common denominator of several algebraic expressions in relation to a given complex fraction. The expressions are (2)(3x-2), (2-4)(5), and (22x+7)(x²-4x+20) and the complex fraction is ((x + 2)(x - 2))(x²). To find the common denominator, we need to consider all the expressions and their factors. Since the complex fraction already includes (x + 2), (x - 2), and (x²) and none of the other expressions introduce new factors that are not already in the complex fraction, the common denominator that includes all possible factors without repetition would be (x + 2)(x - 2)x². Therefore, the correct answer is d) x²(x + 2)(x - 2).