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We are asked to find the value of:

\[
\frac{3x + 1}{x - 4} - \frac{x + 9}{x - 4}
\]

Since both terms have the same denominator \( x - 4 \), we can subtract the numerators directly while keeping the denominator the same.

### Step 1: Subtract the numerators
\[
\frac{(3x + 1) - (x + 9)}{x - 4}
\]

Simplify the numerator:
\[
(3x + 1) - (x + 9) = 3x + 1 - x - 9 = 2x - 8
\]

### Step 2: Write the result
Now, the expression becomes:
\[
\frac{2x - 8}{x - 4}
\]

### Step 3: Factor the numerator (if possible)
\[
\frac{2(x - 4)}{x - 4}
\]

Since \( x - 4 \) appears in both the numerator and the denominator, they cancel out:
\[
2
\]

Thus, the value of the expression is **2**, which corresponds to option **D**.

---

Would you like further details or explanations? Here are some related questions to deepen your understanding:

1. How do you simplify fractions that have the same denominator?
2. Can you describe how factoring helps in simplifying algebraic expressions?
3. What happens when the numerator and denominator of a fraction share a common factor?
4. What should you watch out for when simplifying expressions like this?
5. How would the solution change if the denominators were different?

**Tip:** Always look for common factors in the numerator and denominator to simplify fractions quickly!

What is the value of (3x + 1) / (x - 4) - (x + 9) / (x - 4)?

Learn how to solve the algebraic expression (3x + 1) / (x - 4) - (x + 9) / (x - 4) by subtracting rational expressions with common denominators. Suitable for Grades 7-10.

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