To simplify the expression $\frac{2\sqrt{6} + 2}{2}$, follow these steps:

Step 1: Separate the terms

We can break the expression into two parts:

$\frac{2\sqrt{6}}{2} + \frac{2}{2}$

Step 2: Simplify each part

1. $\frac{2\sqrt{6}}{2} = \sqrt{6}$
2. $\frac{2}{2} = 1$

Final Answer:

$\sqrt{6} + 1$

So, the simplified expression is $\sqrt{6} + 1$.

Let me know if you'd like further clarification or if you have more questions! Here's a few related questions you might find interesting:

1. How can we simplify expressions with square roots in the denominator?
2. What are the properties of square roots in algebra?
3. How do you rationalize a denominator in a fraction like this?
4. Can square roots be simplified further, and if so, when?
5. How can we apply this simplification in more complex equations?

Tip: Always look for common factors when simplifying fractions with multiple terms—breaking them apart can often make simplifications easier!