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: $x = \frac{2}{3}$

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!