What is the following quotient? \( \frac{5}{\sqrt{11}-\sqrt{3}} \)

To rationalize the denominator of \( \frac{5}{\sqrt{11}-\sqrt{3}} \), we multiply both the numerator and the denominator by the conjugate of the denominator, which is \( \sqrt{11} + \sqrt{3} \): \[ \frac{5}{\sqrt{11}-\sqrt{3}} \cdot \frac{\sqrt{11}+\sqrt{3}}{\sqrt{11}+\sqrt{3}} = \frac{5(\sqrt{11} + \sqrt{3})}{(\sqrt{11})^2 - (\sqrt{3})^2} \] Calculating the denominator: \[ (\sqrt{11})^2 - (\sqrt{3})^2 = 11 - 3 = 8 \] So the expression simplifies to: \[ \frac{5(\sqrt{11} + \sqrt{3})}{8} \] Therefore, the final result is: \[ \frac{5(\sqrt{11} + \sqrt{3})}{8} \]