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The given equation is:

\[
\frac{x + 4}{x - 2} = 0
\]

### Solution:

1. To solve the equation, start by setting the numerator equal to zero because a fraction is only equal to zero when its numerator is zero (as long as the denominator is not zero):

   \[
   x + 4 = 0
   \]

2. Solve for \( x \):

   \[
   x = -4
   \]

3. However, we must check if this value of \( x \) makes the denominator zero, because division by zero is undefined. The denominator is \( x - 2 \), so if \( x = 2 \), the denominator would be zero.

4. Since \( x = -4 \) does not make the denominator zero, the solution is valid.

### Final Answer:
\[
x = -4
\]

Would you like any further details or clarification?

Here are some related questions:
1. How do you solve rational equations with variable denominators?
2. What happens if a rational equation has an extraneous solution?
3. How do you handle inequalities involving rational expressions?
4. What is the significance of domain restrictions in rational equations?
5. Can a rational equation have more than one solution?

**Tip:** Always check if the solution makes the denominator zero to avoid undefined expressions.

Solve the rational equation: (x + 4) / (x - 2) = 0.

Find out how to solve the rational equation (x + 4) / (x - 2) = 0. This problem demonstrates the process of setting the numerator to zero and checking for undefined values in the denominator. Ideal for students in Grades 8-10.

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