Let's simplify the expression \( 2x + \frac{2}{2x} \).

1. First, break down each part:
   \[
   2x + \frac{2}{2x}
   \]
   The first term is already in its simplest form.

2. For the second term, simplify \( \frac{2}{2x} \) by canceling out the 2s:
   \[
   \frac{2}{2x} = \frac{1}{x}
   \]

3. Now rewrite the expression:
   \[
   2x + \frac{1}{x}
   \]

This is the simplified form of the expression.

Would you like further clarification or details on this? 

Here are 5 related questions to deepen your understanding:

1. How would you combine terms if the expression were \( 2x - \frac{1}{x} \)?
2. Can you factor \( 2x + \frac{1}{x} \) further in any way?
3. What if you had \( 3x + \frac{2}{x} \)? How would you simplify it?
4. How would you solve \( 2x + \frac{1}{x} = 0 \)?
5. What would happen if you multiplied the entire expression by \( x \)?

**Tip:** Always look for opportunities to cancel out common factors in fractions when simplifying!

Learn how to simplify the algebraic expression 2x + 2/2x with a step-by-step guide. This tutorial explains how to handle fraction simplification and combine algebraic terms, making it ideal for students in Grades 8-10.

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