Question

what is the least common denominator for this rational equation? 15 x 15x 3 5 volver a ver enviar

Explanation:

Step1: Recall LCD of numbers and variables

To find the least common denominator (LCD) for a rational equation (usually involving denominators like 3, 5, 15, and \( x \)), we consider the prime factors of the constant denominators and the variable factors. The constant denominators here (assuming typical denominators like 3, 5, 15) have prime factors: \( 3 = 3 \), \( 5 = 5 \), \( 15 = 3 \times 5 \). For the variable, we have \( x \). The LCD is the product of the highest power of each prime factor and each variable factor. So for constants, the highest power of 3 is 3, highest of 5 is 5, so \( 3 \times 5 = 15 \), and then multiply by \( x \), giving \( 15x \).

Step2: Confirm with options

Among the options (15, \( x \), \( 15x \), 3, 5), \( 15x \) is the product of the LCD of the constant denominators (15) and the variable \( x \), so it's the least common denominator.

Answer:

15x (the option with "15x")