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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.

Find the LCD of \(\frac{3}{x-2}\) and \(\frac{1}{x+3}\)

Learn how to find the Least Common Denominator (LCD) of the rational expressions \(\frac{3}{x-2}\) and \(\frac{1}{x+3}\). This guide provides a step-by-step solution, perfect for students in Grades 8-10 who are studying algebra.

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