Question

determine the lcd of each rational expression $\frac{x + 1}{x - 7}$ $\frac{2x}{x + 3}$
$x - 4$
$2x - 4$
$(x - 7)(x + 3)$
$- 4$

Explanation:

Step1: Recall LCD concept

The least - common denominator (LCD) of two rational expressions with denominators that are non - factorable binomials is the product of those binomials.

Step2: Identify denominators

The denominators of the given rational expressions are \(x - 7\) and \(x + 3\).

Step3: Calculate LCD

The LCD of \(\frac{x + 1}{x - 7}\) and \(\frac{2x}{x+3}\) is \((x - 7)(x + 3)\) since there are no common factors between \(x - 7\) and \(x + 3\).

Answer:

C. \((x - 7)(x + 3)\)