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To solve this problem, we need to find the constant term in the expansion of \( \left(\frac{x}{2} + \frac{2}{x}\right)^6 \).

1. **Using the Binomial Theorem**: The binomial expansion of \( (a + b)^n \) is:
   \[
   \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k
   \]
   For our case:
   - \( a = \frac{x}{2} \)
   - \( b = \frac{2}{x} \)
   - \( n = 6 \)

2. **Setting up the Terms**: In each term of the expansion, the general form is:
   \[
   \binom{6}{k} \left(\frac{x}{2}\right)^{6-k} \left(\frac{2}{x}\right)^k
   \]
   This simplifies to:
   \[
   \binom{6}{k} \cdot \frac{x^{6-k}}{2^{6-k}} \cdot \frac{2^k}{x^k} = \binom{6}{k} \cdot \frac{2^k}{2^{6-k}} \cdot x^{6-2k}
   \]

3. **Finding the Constant Term**: The constant term occurs when the power of \( x \) is zero, so we set the exponent \( 6 - 2k = 0 \).
   - Solving for \( k \):
     \[
     6 - 2k = 0 \Rightarrow k = 3
     \]

4. **Substitute \( k = 3 \) into the Expression**:
   \[
   \binom{6}{3} \cdot \frac{2^3}{2^{6-3}} = \binom{6}{3} \cdot \frac{2^3}{2^3} = \binom{6}{3}
   \]
   Now, calculate \( \binom{6}{3} \):
   \[
   \binom{6}{3} = 20
   \]

5. **Conclusion**: The constant term in the expansion is \( \boxed{20} \).

Would you like further details on any part of this solution?

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### Related Questions:
1. How does the binomial theorem work with fractional terms?
2. What happens if the exponent changes, such as \( (x/2 + 2/x)^8 \)?
3. How do we handle negative terms in binomial expansions?
4. Can the constant term ever be negative in expansions like these?
5. What are the applications of finding constant terms in binomial expansions?

### Tip:
Always check the exponent of the variable in each term to isolate the constant term easily.

Nilai konstanta dari hasil ekspansi \( \left(\frac{x}{2} + \frac{2}{x}\right)^6 \) adalah . . .

Learn how to find the constant term in the expansion of \( \left(\frac{x}{2} + \frac{2}{x}\right)^6 \) using the binomial theorem. This problem involves understanding binomial expansion and finding terms with zero exponent in x. Suitable for high school students in Grades 10-12.

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