To solve the equation:

\[
\frac{18}{x} + 3 = \frac{6}{x} - 3
\]

### Step 1: Eliminate the fractions by multiplying through by \( x \).
Multiply both sides of the equation by \( x \) (assuming \( x \neq 0 \)):

\[
x \cdot \left( \frac{18}{x} + 3 \right) = x \cdot \left( \frac{6}{x} - 3 \right)
\]

This simplifies to:

\[
18 + 3x = 6 - 3x
\]

### Step 2: Combine like terms.
Move all terms involving \( x \) to one side and constants to the other:

\[
3x + 3x = 6 - 18
\]

Simplifying:

\[
6x = -12
\]

### Step 3: Solve for \( x \).

\[
x = \frac{-12}{6} = -2
\]

### Final Answer:
\[
x = -2
\]

Would you like more details on any step?

Here are 5 related questions:
1. How do you check the solution to a rational equation?
2. What happens if you multiply both sides of an equation by 0?
3. Can there be more than one solution for a rational equation?
4. What is the domain of a rational function?
5. How do you solve an equation involving variables in both the numerator and denominator?

**Tip:** Always verify your solutions in the original equation to ensure they do not make any denominators equal to zero!

Learn how to solve the rational equation 18/x + 3 = 6/x - 3 with a step-by-step solution. This problem covers essential algebraic concepts, including eliminating fractions by multiplying through by the denominator and solving for x. Suitable for students in Grades 8-10.

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