To rationalize the denominator of the expression \(\frac{11}{\sqrt{5} - 2}\), we can multiply the numerator and the denominator by the conjugate of the denominator, which is \(\sqrt{5} + 2\).
Here’s how we do it step by step:
\[ \frac{11}{\sqrt{5} - 2} \cdot \frac{\sqrt{5} + 2}{\sqrt{5} + 2} = \frac{11(\sqrt{5} + 2)}{(\sqrt{5} - 2)(\sqrt{5} + 2)} \]
Now, simplify the denominator:
\[ (\sqrt{5} - 2)(\sqrt{5} + 2) = \sqrt{5}^2 - 2^2 = 5 - 4 = 1 \]
Now substituting back, we have:
\[ \frac{11(\sqrt{5} + 2)}{1} = 11(\sqrt{5} + 2) \]
Thus, the rationalized form of the expression is:
\[ 11\sqrt{5} + 22 \]
So, the final answer is:
\[ \frac{11}{\sqrt{5} - 2} = 11\sqrt{5} + 22 \]