The expression you've provided can be interpreted in two ways, depending on how it's structured. Let's clarify:

1. If it is meant as:
   \[
   3x + \frac{12}{x} + 4
   \]
   Then this expression cannot be simplified further, as it involves a sum of terms. However, you could evaluate it for specific values of \(x\).

2. If it is meant as:
   \[
   \frac{3x + 12}{x + 4}
   \]
   This is a rational expression that can be simplified.

### Simplifying \( \frac{3x + 12}{x + 4} \):
Factor the numerator:
\[
\frac{3(x + 4)}{x + 4}
\]
If \(x \neq -4\), you can cancel out the common factor \(x + 4\), leaving:
\[
3
\]

So, the simplified expression is \(3\), as long as \(x \neq -4\).

Would you like more details, or do you have any questions about this process?

---

Here are 5 related questions:
1. How do you factor common terms in algebraic expressions?
2. What happens when \(x = -4\) in this expression?
3. How can you evaluate this expression for specific values of \(x\)?
4. What are rational expressions, and how do you simplify them?
5. How would this expression change if it were a fraction subtraction instead?

**Tip**: Always check for values of \(x\) that make the denominator zero in rational expressions to avoid undefined values.

This guide explains how to simplify the rational expression (3x + 12) / (x + 4) by factoring the numerator and canceling out common terms. It includes steps to handle algebraic fractions and addresses potential undefined values when the denominator is zero. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation