Question

Rationalize the numerator:

Answer 1

Have you tried multiplying by the conjugate?

Answer 2

\[\frac{\left(\sqrt{11}+\sqrt{13}\right) \left(\sqrt{11}-\sqrt{13}\right)}{2 \left(\sqrt{11}-\sqrt{13}\right)}=-\frac{2}{2 \left(\sqrt{11}-\sqrt{13}\right)}=-\frac{1}{\sqrt{11}-\sqrt{13}} \]