Identify the \( L C D \) in the equation below. \( \frac{x}{x^{2}-16}+\frac{12}{x-4}=\frac{8}{x+4} \) \( x+4 \) \( (x+4)^{2} \) \( x^{2}-16 \) \( x-4 \)

To identify the least common denominator (LCD) in the given equation, we need to consider the denominators present in the fractions. We have \( x^{2}-16 \) which can be factored into \( (x-4)(x+4) \). Thus, the denominators are \( x^{2}-16 \) and \( x-4 \). The least common denominator takes into account all unique factors from each denominator at their highest powers. Here, \( x^{2}-16 \) already includes both \( x-4 \) and \( x+4 \) as factors, making it the most comprehensive choice. Therefore, the LCD is \( x^{2}-16 \). Additionally, remember that factoring your denominators can often simplify finding the LCD and clarifying your algebraic operations. Don't forget to check for restrictions as well; for this equation, \( x \neq 4 \) and \( x \neq -4 \) to prevent division by zero!