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To solve the expression \( \frac{6}{x - 3} + \frac{8}{x - 6} \), let's find a common denominator and simplify:

### Step-by-Step Solution

1. **Identify the Common Denominator:**
   The denominators are \( x - 3 \) and \( x - 6 \), so the common denominator is \( (x - 3)(x - 6) \).

2. **Rewrite Each Fraction with the Common Denominator:**
   \[
   \frac{6}{x - 3} = \frac{6(x - 6)}{(x - 3)(x - 6)} = \frac{6x - 36}{(x - 3)(x - 6)}
   \]
   \[
   \frac{8}{x - 6} = \frac{8(x - 3)}{(x - 3)(x - 6)} = \frac{8x - 24}{(x - 3)(x - 6)}
   \]

3. **Combine the Two Fractions:**
   \[
   \frac{6x - 36}{(x - 3)(x - 6)} + \frac{8x - 24}{(x - 3)(x - 6)} = \frac{(6x - 36) + (8x - 24)}{(x - 3)(x - 6)}
   \]

4. **Simplify the Numerator:**
   Combine like terms in the numerator:
   \[
   (6x - 36) + (8x - 24) = 14x - 60
   \]
   So the expression becomes:
   \[
   \frac{14x - 60}{(x - 3)(x - 6)}
   \]

5. **Factor the Denominator:**
   Notice that \( (x - 3)(x - 6) = x^2 - 9x + 18 \). So we have:
   \[
   \frac{14x - 60}{x^2 - 9x + 18}
   \]

### Final Answer
The expression equivalent to \( \frac{6}{x - 3} + \frac{8}{x - 6} \) is:
\[
\frac{14x - 60}{x^2 - 9x + 18}
\]
Therefore, the correct answer is:

**A.** \( \frac{14x - 60}{x^2 - 9x + 18} \)

Would you like further details or have any questions?

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### Related Questions

1. How do you find a common denominator for adding fractions?
2. What are some techniques for factoring quadratic expressions?
3. How can simplifying rational expressions help in algebra?
4. How can you verify the answer by substituting values for \( x \)?
5. What is the importance of combining like terms in algebra?

### Tip:
When adding or subtracting fractions, always look for the least common denominator to simplify the process.

Which expression is equivalent to \( \frac{6}{x - 3} + \frac{8}{x - 6} \)?

Solve the algebra problem to find an equivalent expression for \( \frac{6}{x - 3} + \frac{8}{x - 6} \) by finding a common denominator and simplifying the expression. Includes detailed steps on factoring and combining terms, suitable for Grades 9-11.

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