To simplify the expressions by rationalizing the denominators, we multiply both the numerator and the denominator by the conjugate of the denominator. Below are solutions for some of the given problems:

11. \(\frac{-ab}{\sqrt{a} - \sqrt{b}}\)

Multiply top and bottom by the conjugate, \(\sqrt{a} + \sqrt{b}\):

\[
\frac{-ab(\sqrt{a} + \sqrt{b})}{(\sqrt{a} - \sqrt{b})(\sqrt{a} + \sqrt{b})} = \frac{-ab(\sqrt{a} + \sqrt{b})}{a - b}
\]

12. \(\frac{x + \sqrt{x}}{\sqrt{x} - 1}\)

Multiply top and bottom by the conjugate, \(\sqrt{x} + 1\):

\[
\frac{(x + \sqrt{x})(\sqrt{x} + 1)}{(\sqrt{x} - 1)(\sqrt{x} + 1)} = \frac{(x + \sqrt{x})(\sqrt{x} + 1)}{x - 1}
\]

13. \(\frac{x + \sqrt{xy}}{\sqrt{x} - \sqrt{y}}\)

Multiply top and bottom by the conjugate, \(\sqrt{x} + \sqrt{y}\):

\[
\frac{(x + \sqrt{xy})(\sqrt{x} + \sqrt{y})}{(\sqrt{x} - \sqrt{y})(\sqrt{x} + \sqrt{y})} = \frac{(x + \sqrt{xy})(\sqrt{x} + \sqrt{y})}{x - y}
\]

14. \(\frac{1 + \sqrt{a}}{2 - \sqrt{a}}\)

Multiply top and bottom by the conjugate, \(2 + \sqrt{a}\):

\[
\frac{(1 + \sqrt{a})(2 + \sqrt{a})}{(2 - \sqrt{a})(2 + \sqrt{a})} = \frac{2 + 2\sqrt{a} + a + \sqrt{a}}{4 - a}
\]

15. \(\frac{1}{\sqrt{x} - \sqrt{y}}\)

Multiply top and bottom by the conjugate, \(\sqrt{x} + \sqrt{y}\):

\[
\frac{1 \cdot (\sqrt{x} + \sqrt{y})}{(\sqrt{x} - \sqrt{y})(\sqrt{x} + \sqrt{y})} = \frac{\sqrt{x} + \sqrt{y}}{x - y}
\]

Continue with similar steps for the remaining expressions to rationalize the denominators.