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To find the Least Common Denominator (LCD) for the given expression:

\[
\frac{5x + 1}{2} + \frac{x - 3}{3}
\]

### Steps to Find the LCD:

1. **Identify the denominators**: The denominators in this expression are \(2\) and \(3\).

2. **Find the Least Common Multiple (LCM)** of the denominators:
   - List the multiples of 2: \(2, 4, 6, 8, 10, \dots\)
   - List the multiples of 3: \(3, 6, 9, 12, 15, \dots\)

   The smallest multiple that both 2 and 3 share is \(6\). Therefore, the LCD is \(6\).

### Next Steps:

- Rewrite each fraction with the denominator as \(6\).

\[
\frac{5x + 1}{2} = \frac{3(5x + 1)}{6} = \frac{15x + 3}{6}
\]
\[
\frac{x - 3}{3} = \frac{2(x - 3)}{6} = \frac{2x - 6}{6}
\]

- Now, the expression can be combined:

\[
\frac{15x + 3}{6} + \frac{2x - 6}{6} = \frac{(15x + 3) + (2x - 6)}{6} = \frac{17x - 3}{6}
\]

Would you like more details on these steps, or do you have any questions?

### Related Questions:

1. How do you find the LCD of more than two fractions?
2. What happens if the denominators are polynomials instead of integers?
3. How do you simplify complex fractions using the LCD?
4. Can the LCD be used to solve equations involving fractions?
5. What is the importance of the LCD in adding and subtracting fractions?

### Tip:
Always factor the denominators first if they are polynomials before finding the LCD to ensure you capture the correct common factors.

How to get the least common denominator (LCD) for the expression (5x + 1)/2 + (x - 3)/3?

Learn how to find the least common denominator (LCD) for the algebraic expression (5x + 1)/2 + (x - 3)/3. This problem covers key algebraic concepts such as finding the LCM and adding fractions. Suitable for students in Grades 7-9.

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