The equation \( 3 - \frac{2}{x} = \frac{4}{x} \) is a rational equation because it contains terms with variables in the denominator. Let's solve it step by step.

### Steps:

1. **Clear the fractions**:
   Multiply both sides of the equation by \( x \) (assuming \( x \neq 0 \)) to eliminate the denominators:

   \[
   x \left( 3 - \frac{2}{x} \right) = x \cdot \frac{4}{x}
   \]

   This simplifies to:

   \[
   3x - 2 = 4
   \]

2. **Solve the simplified linear equation**:
   Add 2 to both sides to isolate the term with \( x \):

   \[
   3x = 6
   \]

3. **Divide by 3**:

   \[
   x = 2
   \]

So, the solution to the equation is \( x = 2 \).

### Check the solution:

Substitute \( x = 2 \) back into the original equation to verify:

\[
3 - \frac{2}{2} = \frac{4}{2}
\]
\[
3 - 1 = 2
\]
\[
2 = 2
\]

Since both sides are equal, the solution is correct.

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Would you like more details or have any questions? Here are some related questions to explore:

1. What are the properties of rational functions?
2. How do you solve rational equations with different denominators?
3. Can you always multiply by the variable to clear denominators in rational equations?
4. How do you handle undefined values for rational equations?
5. What happens when there are multiple solutions in a rational equation?

**Tip**: Always check for restrictions on the variable (e.g., \( x \neq 0 \)) when solving rational equations.

Learn how to solve the rational equation 3 - 2/x = 4/x with a detailed step-by-step solution. This problem covers key algebraic concepts, including clearing fractions and solving linear equations. Suitable for students in Grades 8-10.

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