Let's solve the equation:

\[
\frac{2x}{x+1} + \frac{5}{2x} = 2
\]

### Step 1: Find a common denominator
The least common denominator (LCD) of \( x+1 \) and \( 2x \) is \( 2x(x+1) \). Multiply each term by this LCD to eliminate the denominators:

\[
2x(x+1) \left( \frac{2x}{x+1} \right) + 2x(x+1) \left( \frac{5}{2x} \right) = 2 \cdot 2x(x+1)
\]

This simplifies to:

\[
2x \cdot 2x + (x+1) \cdot 5 = 2 \cdot 2x(x+1)
\]

### Step 2: Simplify the equation
Simplifying each term:

\[
4x^2 + 5(x+1) = 4x(x+1)
\]

Distribute the 5 and the 4x:

\[
4x^2 + 5x + 5 = 4x^2 + 4x
\]

### Step 3: Cancel out \( 4x^2 \)
Subtract \( 4x^2 \) from both sides:

\[
5x + 5 = 4x
\]

### Step 4: Solve for \( x \)
Now, subtract \( 4x \) from both sides:

\[
x + 5 = 0
\]

So, \( x = -5 \).

### Solution:
The solution to the equation is:

\[
x = -5
\]

Would you like further details, or do you have any questions?

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Here are 5 related questions to expand your understanding:
1. What happens if you try to solve a similar equation with more complex denominators?
2. How does solving this type of rational equation differ from solving linear equations?
3. How do you determine if there are any extraneous solutions in rational equations?
4. What is the importance of finding the least common denominator (LCD)?
5. Can you solve this equation graphically by plotting the functions?

**Tip:** Always check if your solutions cause any division by zero in the original equation when working with rational equations.

Learn how to solve the rational equation 2x/(x+1) + 5/(2x) = 2 with a detailed, step-by-step solution. This guide covers key algebraic concepts, including finding the least common denominator and simplifying rational expressions, ideal for students in Grades 9-11.

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