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The expression you have shared is:

\[
\frac{\sqrt[5]{30 + \sqrt[3]{8}}}{\sqrt[5]{245 - \sqrt[3]{8}}}
\]

### Step-by-step solution:

1. **Simplify the cube roots (∛)**:
   \[
   \sqrt[3]{8} = 2
   \]

2. **Substitute ∛8 into the equation**:

   The expression now becomes:
   \[
   \frac{\sqrt[5]{30 + 2}}{\sqrt[5]{245 - 2}} = \frac{\sqrt[5]{32}}{\sqrt[5]{243}}
   \]

3. **Simplify the fifth roots (∜)**:

   - \(\sqrt[5]{32} = 2\), since \(2^5 = 32\)
   - \(\sqrt[5]{243} = 3\), since \(3^5 = 243\)

4. **Final simplified form**:
   \[
   \frac{2}{3}
   \]

So, the result of the expression is \( \frac{2}{3} \).

---

Would you like more details on any specific step? Here are 5 related questions you might find interesting:

1. What are the general steps for simplifying radical expressions?
2. How do you calculate cube roots and fifth roots?
3. What are the properties of exponents and roots that can help in simplifying expressions?
4. How can this type of problem be extended to complex numbers?
5. What would the answer be if the powers were different?

**Tip:** Remember that understanding how to manipulate exponents and roots is key to mastering algebraic simplifications.

Simplify the expression: \( \frac{\sqrt[5]{30 + \sqrt[3]{8}}}{\sqrt[5]{245 - \sqrt[3]{8}}} \)

Learn how to simplify a complex radical expression involving fifth and cube roots. This example covers how to handle exponents and radicals step-by-step, making it ideal for students in Grades 10-12.

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