Rationalise the denominator : `(5)/(sqrt(11)+4)`.

Explanation

To rationalize the denominator of the expression \(\frac{5}{\sqrt{11} + 4}\), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Denominator**:
The denominator is \(\sqrt{11} + 4\).

2. **Find the Conjugate**:
The conjugate of \(\sqrt{11} + 4\) is \(\sqrt{11} - 4\).

3. **Multiply by the Conjugate**:
To rationalize the denominator, multiply both the numerator and the denominator by the conjugate:
\[ \frac{5}{\sqrt{11} + 4} \cdot \frac{\sqrt{11} - 4}{\sqrt{11} - 4} \]

4. **Rewrite the Expression**:
This gives us:
\[ \frac{5(\sqrt{11} - 4)}{(\sqrt{11} + 4)(\sqrt{11} - 4)} \]

5. **Simplify the Denominator**:
The denominator can be simplified using the difference of squares formula \(a^2 - b^2\):
\[ (\sqrt{11})^2 - (4)^2 = 11 - 16 = -5 \]

6. **Combine the Numerator**:
The numerator becomes:
\[ 5(\sqrt{11} - 4) = 5\sqrt{11} - 20 \]

7. **Final Expression**:
Now, we can write the expression as:
\[ \frac{5\sqrt{11} - 20}{-5} \]

8. **Simplify the Expression**:
Dividing each term in the numerator by \(-5\):
\[ -\sqrt{11} + 4 = 4 - \sqrt{11} \]

### Final Answer:
The rationalized form of \(\frac{5}{\sqrt{11} + 4}\) is:
\[ 4 - \sqrt{11} \]