The given expression:

$\frac{\sqrt{6} + \sqrt{8}}{\sqrt{6} + \sqrt{2}}$

simplifies to:

$\frac{1}{2} + \frac{\sqrt{3}}{2}$

Would you like more details or explanations about this simplification?

Here are 5 related questions you might find interesting:

1. How do you rationalize the denominator of a radical expression?
2. Can you explain the process of simplifying square roots like $\sqrt{8}$?
3. What happens when you multiply expressions with radicals?
4. How do you handle irrational numbers in the numerator and denominator?
5. How is this simplification useful in trigonometry or algebraic functions?

Tip: Always look for common factors in radicals to simplify them before performing further operations!