Question: Question 5, 6.2.37 HW Score: 14.29 Points: 0 of 1 Assume that the expressions given are…

Question 5, 6.2.37 HW Score: 14.29 Points: 0 of 1

Assume that the expressions given are denominators of fractions. Find the least common denominator (LCD) for the group.

9c + 4t, 8t^2 - 16t^2, 9c - 4t

The least common denominator is [].

Solution

Step 1: Factor each denominator.

\[ 8t^2 - 16t^2 = -8t^2 \]

\[ 9c + 4t \text{ and } 9c - 4t \text{ are already in simplest form} \]

Step 2: Identify the least common denominator (LCD) by finding the product of the distinct factors.

\[ \text{LCD} = (9c + 4t)(9c - 4t)(8t^2) \]

Step 3: Simplify the LCD expression if possible.

\[ \text{LCD} = 8t^2 (81c^2 - 16t^2) \]

The least common denominator is \(8t^2 (81c^2 - 16t^2)\).