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It seems like you've uploaded an image with several math problems. Let me analyze and extract the text for better readability and understanding:

1. **Simple Rational Equation: Solve for \( x \)**  
   \[
   \frac{2}{x} = 3
   \]

2. **Rational Equation with Quadratic Terms: Solve for \( x \)**  
   \[
   \frac{1}{x-2} + \frac{1}{x+2} = \frac{2}{x^2-4}
   \]

3. **Rational Equation with Multiple Variables: Solve for \( x \)**  
   \[
   \frac{1}{x-2} + \frac{1}{x+2} = \frac{2x}{x^2-4}
   \]

4. **Rational Equation with a Binomial: Solve for \( x \)**  
   \[
   \frac{3}{2x+1} = \frac{2x-3}{2x+1}
   \]

5. **Complex Rational Equation: Solve for \( x \)**  
   \[
   \frac{2x}{x-2} = \frac{3x}{x+2} - \frac{5}{x^2-4}
   \]

Let me begin by solving these problems for you one by one.

### 1. Simple Rational Equation: \( \frac{2}{x} = 3 \)

To solve for \( x \), we can multiply both sides by \( x \) to eliminate the denominator:
\[
2 = 3x
\]
Now divide both sides by 3:
\[
x = \frac{2}{3}
\]

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Would you like me to continue solving the rest of the equations in sequence, or would you like to focus on a specific one?

Here are some related questions to think about:
1. How do you solve rational equations with different denominators?
2. What happens if \( x \) makes any denominator zero?
3. How can factoring help in solving complex rational equations?
4. What are the key steps for simplifying complex fractions?
5. How does cross-multiplication work in rational equations?

**Tip:** Always check your solutions by substituting them back into the original equation, especially for rational equations where extraneous solutions may arise!

Solve the following rational equations:
1. Simple Rational Equation: Solve for x: 2/x = 3
2. Rational Equation with Quadratic Terms: Solve for x: 1/(x-2) + 1/(x+2) = 2/(x^2-4)
3. Rational Equation with Multiple Variables: Solve for x: 1/(x-2) + 1/(x+2) = 2x/(x^2-4)
4. Rational Equation with a Binomial: Solve for x: 3/(2x+1) = (2x-3)/(2x+1)
5. Complex Rational Equation: Solve for x: 2x/(x-2) = 3x/(x+2) - 5/(x^2-4)

Learn how to solve a variety of rational equations, including those with quadratic terms, multiple variables, and binomials. This detailed solution set covers key algebraic concepts, factoring, and cross-multiplication. Suitable for students in Grades 9-12.

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