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To rationalize the denominator of \(\frac{\sqrt{11}}{\sqrt{11} - 2}\), we need to eliminate the square root in the denominator. We can do this by multiplying both the numerator and the denominator by the conjugate of the denominator, \(\sqrt{11} + 2\).

Here are the steps:

1. **Original Expression**:
   \[
   \frac{\sqrt{11}}{\sqrt{11} - 2}
   \]

2. **Multiply by the Conjugate**:
   Multiply both the numerator and the denominator by \(\sqrt{11} + 2\):
   \[
   \frac{\sqrt{11} \cdot (\sqrt{11} + 2)}{(\sqrt{11} - 2)(\sqrt{11} + 2)}
   \]

3. **Expand the Numerator**:
   \[
   \sqrt{11} \cdot \sqrt{11} + \sqrt{11} \cdot 2 = 11 + 2\sqrt{11}
   \]

4. **Expand the Denominator**:
   The denominator is a difference of squares:
   \[
   (\sqrt{11} - 2)(\sqrt{11} + 2) = (\sqrt{11})^2 - (2)^2 = 11 - 4 = 7
   \]

5. **Combine**:
   Now we have:
   \[
   \frac{11 + 2\sqrt{11}}{7}
   \]

6. **Final Answer**:
   \[
   \frac{11 + 2\sqrt{11}}{7}
   \]

So, the rationalized form of \(\frac{\sqrt{11}}{\sqrt{11} - 2}\) in its simplest form is:
\[
\frac{11 + 2\sqrt{11}}{7}
\]

Would you like further details or have any questions?

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### Related Questions:
1. How do you rationalize a denominator with complex conjugates?
2. Why does rationalizing the denominator help in simplifying expressions?
3. What are the benefits of using conjugates in rationalization?
4. Can you apply the same method if the denominator is \(\sqrt{a} - b\)?
5. How can we extend this method to denominators with multiple terms involving square roots?

### Tip:
When rationalizing a denominator, always consider multiplying by the conjugate, especially if it has two terms with a square root.

Rationalise the denominator of \(\frac{\sqrt{11}}{\sqrt{11} - 2}\). Give your answer in its simplest form.

Learn how to rationalize the denominator of \(\frac{\sqrt{11}}{\sqrt{11} - 2}\) with a step-by-step solution. This problem explores key algebraic concepts, including rationalization and the difference of squares formula. Suitable for students in Grades 9-11.

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