We are given the equation:

\[
\frac{7}{4x} - \frac{3}{x^2} = \frac{1}{2x^2}
\]

### Step 1: Find the common denominator
The denominators are \(4x\), \(x^2\), and \(2x^2\). To simplify the equation, the least common denominator (LCD) is \(4x^2\). We'll multiply both sides of the equation by \(4x^2\) to eliminate the fractions.

Multiplying each term by \(4x^2\), we get:

\[
\left( \frac{7}{4x} \right) \cdot 4x^2 - \left( \frac{3}{x^2} \right) \cdot 4x^2 = \left( \frac{1}{2x^2} \right) \cdot 4x^2
\]

### Step 2: Simplify each term
- First term: \(\frac{7}{4x} \cdot 4x^2 = 7x\)
- Second term: \(\frac{3}{x^2} \cdot 4x^2 = 12\)
- Third term: \(\frac{1}{2x^2} \cdot 4x^2 = 2\)

Now, the equation becomes:

\[
7x - 12 = 2
\]

### Step 3: Solve for \(x\)
Add 12 to both sides:

\[
7x = 14
\]

Divide by 7:

\[
x = 2
\]

### Final Answer:
The solution is \(x = 2\).

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

Here are five related questions:
1. How do you find the least common denominator in similar equations?
2. Can you solve a similar equation where the constants are different?
3. How do you handle equations involving higher powers of \(x\)?
4. What are other methods to solve equations with fractions?
5. What if the solution involves negative values of \(x\)?

**Tip:** Always check your solution by substituting back into the original equation to verify.

This tutorial solves the rational equation 7/4x - 3/x² = 1/2x² by finding the least common denominator and simplifying step by step. The solution includes detailed explanations suitable for high school students (Grades 9-12), covering key algebraic concepts and methods for dealing with equations involving fractions.

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