Question

question #3
determine the least common denominator of the following rational expressions:
\\(\frac{x + 3}{x^{2}-5x + 4}\\) and \\(\frac{2x}{x - 1}\\)
\\(\circ(x + 4)(x + 1)\\)
\\(\circ(x - 4)(x - 1)\\)
\\(\circ(x - 1)\\)
\\(\circ(x - 4)(x - 1)(x - 1)\\)

Explanation:

Step1: Factor the first denominator

Factor $x^{2}-5x + 4$. We find two numbers that multiply to $4$ and add up to $-5$. These numbers are $-4$ and $-1$. So $x^{2}-5x + 4=(x - 4)(x - 1)$.

Step2: Determine the LCM of denominators

The denominators are $(x - 4)(x - 1)$ and $x - 1$. The least - common multiple of these two expressions is $(x - 4)(x - 1)$ since it contains all the unique factors of each denominator with the highest power of each factor.

Answer:

$(x - 4)(x - 1)$