To solve the equation \(\frac{x - 4}{x + 2} = 3\), follow these steps:

1. **Multiply both sides by \((x + 2)\)** to eliminate the denominator:
   \[
   \frac{x - 4}{x + 2} \cdot (x + 2) = 3 \cdot (x + 2)
   \]
   This simplifies to:
   \[
   x - 4 = 3(x + 2)
   \]

2. **Distribute the 3 on the right side**:
   \[
   x - 4 = 3x + 6
   \]

3. **Move all terms involving \(x\)** to one side of the equation and constant terms to the other side:
   \[
   x - 3x = 6 + 4
   \]
   Simplifying this gives:
   \[
   -2x = 10
   \]

4. **Solve for \(x\)** by dividing both sides by \(-2\):
   \[
   x = \frac{10}{-2} = -5
   \]

So, the solution is \(x = -5\).

Would you like further details on any step? Here are some related questions:

1. How do you handle more complex fractions in equations?
2. What is the general approach to solving rational equations?
3. Could you explain how to check if a solution is valid?
4. What happens if the solution makes the denominator zero?
5. How can you solve equations involving multiple fractions?

**Tip:** Always check if your solution is valid by substituting it back into the original equation.

Learn how to solve the rational equation (x - 4) / (x + 2) = 3 with a detailed step-by-step solution. This problem covers key algebraic concepts, including rational equations and solving techniques. Suitable for high school students.

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