https://file.aiquickdraw.com/mathbot/file/1728524665634cj7zod3w.jpg

The problem shown asks to find the Least Common Denominator (LCD) of two rational expressions: 

\[
\frac{7}{x+6} \quad \text{and} \quad \frac{2}{x-6}.
\]

### Step-by-Step Solution:

1. **Identify the denominators:**
   The denominators are \(x + 6\) and \(x - 6\).

2. **Analyze the denominators:**
   Since \(x + 6\) and \(x - 6\) are both linear and don't share any common factors, the least common denominator is simply the product of these two expressions.

3. **Multiply the denominators:**
   The LCD is:

   \[
   (x+6)(x-6) = x^2 - 36.
   \]

Thus, the least common denominator (LCD) is \(x^2 - 36\).

Would you like further details or have any questions?

### Related Questions:
1. How would you find the LCD for expressions with quadratic denominators?
2. What happens if one of the denominators had a common factor with the other?
3. How would you simplify a rational expression once the LCD is found?
4. How can you find the LCD if one denominator is a constant?
5. What is the next step after finding the LCD if you want to add the two rational expressions?

### Tip:
When finding the LCD for rational expressions, always look for common factors between denominators first before multiplying them. This can simplify the process.

What is the least common denominator of 7/(x+6) and 2/(x-6)?

This guide explains how to find the least common denominator (LCD) of rational expressions with linear denominators, using the example of 7/(x+6) and 2/(x-6). Key algebraic concepts include rational expressions and the difference of squares formula. Suitable for students in Grades 8-10.

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