Question

question #10
which of the following factors will be included in the least common denominator of the rational expressions? select all that apply.
\frac{-7x}{5x^{2}-10x} and \frac{3}{x - 2}
□ -7x
□ 3
□ 5x
□ x - 2

Explanation:

Step1: Factor the first - denominator

Factor $5x^{2}-10x$ as $5x(x - 2)$.

Step2: Find the LCM of denominators

The denominators are $5x(x - 2)$ and $x - 2$. The least - common denominator (LCD) is the product of the unique factors, each raised to the highest power to which it occurs in any of the denominators. Here, the unique factors are $5$, $x$, and $x - 2$.

Answer:

C. $5x$, D. $x - 2$