The problem asks to find the Least Common Denominator (LCD) of the fractions $\frac{3}{x-2}$ and $\frac{1}{x+3}$.

Step-by-Step Solution:

1. Identify the denominators:

   • The first fraction has the denominator $x - 2$.
   • The second fraction has the denominator $x + 3$.

2. Determine the LCD:

   • The LCD is the least common multiple (LCM) of the denominators.
   • Since $x - 2$ and $x + 3$ are distinct linear factors, the LCD is simply the product of these two factors.

   $\text{LCD} = (x - 2)(x + 3)$

So, the LCD of the fractions $\frac{3}{x-2}$ and $\frac{1}{x+3}$ is $(x - 2)(x + 3)$.

Would you like to dive deeper into this topic or have any other questions?

Here are five related questions:

1. How do you find the LCD of more than two fractions?
2. What is the importance of finding the LCD in adding fractions?
3. How can you simplify the expression $\frac{1}{x-2} + \frac{1}{x+3}$ using the LCD?
4. What happens if one of the denominators is a quadratic expression?
5. Can the LCD ever be smaller than any of the original denominators?

Tip: When dealing with algebraic fractions, always factor the denominators first to find the LCD efficiently.