Question

What is the least common denominator of the rational expressions below 2/x^2-7/4x^2+12x

A. 4x^3(x+3)
B. 4x^2(x+3)
C. x^2(x+3)
D. x^3(x+3)

Answer 1

2²·x²·(x+3) = 4x²(x+3)

Explanation:

Answer 2

Answer: option B. 4x²(x+3)

Explanation:

The least common denominator is the product of the prime factors, each raised to the highest power with which in appears among the denominators.

1. The rational expressions written properly are:

`(2)/(x^2) \\ \\ -(7)/(4x^2+12x)`

2. Factor each denominator:

a) x² is alreaday factored

b) 4x² + 12x = 4x(x + 3) = 2²·x (x + 3)

3. Use each factor:

Use each factor once, raised to the highest power with which it appears, to form the product. These are: x², 2², and (x+3)

⇒ 2²·x²·(x+3) = 4x²(x+3)

And that is the least common denominator.