Question

question #7
which of the following factors will be included in the least common denominator of the rational expressions? select all that apply.
\frac{2x - 1}{3x^{2}+5x + 2} and \frac{x - 6}{x + 1}
□ x + 1
□ x - 6
□ 2x - 1
□ 3x + 2

Explanation:

Step1: Factor the first - denominator

Factor $3x^{2}+5x + 2$. We have $3x^{2}+5x + 2=3x^{2}+3x+2x + 2=3x(x + 1)+2(x + 1)=(3x + 2)(x + 1)$.

Step2: Determine the LCM of denominators

The denominators are $(3x + 2)(x + 1)$ and $x + 1$. The least - common denominator (LCD) is the product of all unique factors, each raised to the highest power to which it occurs in any of the denominators. The unique factors are $x + 1$ and $3x+2$.

Answer:

A. $x + 1$
D. $3x + 2$