To solve the expression \( \frac{14 + 6\sqrt{5} + 7 - 3\sqrt{5}}{8} \), let's break it down step by step.

1. **Combine like terms:**
   \[
   (14 + 7) + (6\sqrt{5} - 3\sqrt{5}) = 21 + 3\sqrt{5}
   \]

2. **Rewrite the expression:**
   \[
   \frac{21 + 3\sqrt{5}}{8}
   \]

3. **Separate the terms:**
   \[
   \frac{21}{8} + \frac{3\sqrt{5}}{8}
   \]

So, the simplified result is:
\[
\frac{21}{8} + \frac{3\sqrt{5}}{8}
\]

This is the final simplified form.

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Learn how to simplify the expression (14 + 6√5 + 7 - 3√5) divided by 8, combining like terms and simplifying radical expressions step-by-step. This problem is suitable for students in Grades 8-10, covering key concepts in algebra and radical simplification.

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