Questions: Rationalize the denominator. 5 / (3 + √11) 5 / (3 + √11) = (Simplify your answer. Type an exact answer, using radicals)

Rationalize the denominator of the expression \( \frac{5}{3+\sqrt{11}} \).

Multiply by the conjugate.

To rationalize the denominator, we multiply both the numerator and the denominator by the conjugate \( 3 - \sqrt{11} \): \[ \frac{5}{3+\sqrt{11}} \cdot \frac{3-\sqrt{11}}{3-\sqrt{11}} = \frac{5(3-\sqrt{11})}{(3+\sqrt{11})(3-\sqrt{11})} \]

Simplify the denominator.

The denominator simplifies as follows: \[ (3+\sqrt{11})(3-\sqrt{11}) = 3^2 - (\sqrt{11})^2 = 9 - 11 = -2 \]

Simplify the numerator.

The numerator simplifies to: \[ 5(3-\sqrt{11}) = 15 - 5\sqrt{11} \]

Combine the results.

Thus, the expression becomes: \[ \frac{15 - 5\sqrt{11}}{-2} = -\frac{15}{2} + \frac{5\sqrt{11}}{2} \]

The rationalized form of \( \frac{5}{3+\sqrt{11}} \) is \( -\frac{15}{2} + \frac{5\sqrt{11}}{2} \).

The final answer is \\(\boxed{-\frac{15}{2} + \frac{5\sqrt{11}}{2}}\\).