Thank you for the clarification! The expression you're referring to is:

$\frac{1 + \sqrt{2}}{\sqrt{5}}$

Step 1: Rationalize the denominator

To rationalize the denominator, multiply both the numerator and the denominator by $\sqrt{5}$:

$\frac{1 + \sqrt{2}}{\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}} = \frac{(1 + \sqrt{2}) \times \sqrt{5}}{5}$

Step 2: Simplify the numerator

Distribute $\sqrt{5}$ in the numerator:

$\frac{\sqrt{5} + \sqrt{10}}{5}$

Denominator

The denominator of the simplified expression is $5$.

Would you like more details or have any questions?

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Here are some related questions for further practice:

1. How do you rationalize the denominator of a more complex fraction?
2. How do you distribute a square root across terms in a binomial?
3. What are the steps to simplify a fraction with a binomial in the numerator?
4. Can you rationalize a denominator if it is a complex number?
5. How does rationalizing affect the value of the original expression?

Tip: Always ensure each term in the numerator is multiplied by the factor used to rationalize the denominator.