Answer:
[tex]-11\sqrt{5}-11\sqrt{6}[/tex]
Step-by-step explanation:
The given radical expression is;
[tex]\frac{11}{\sqrt{5}-\sqrt{6}}[/tex]
We multiply both the numerator and the denominator by the conjugate of
[tex]\sqrt{5}-\sqrt{6}[/tex] which is [tex]\sqrt{5}+\sqrt{6}[/tex]
[tex]\frac{11(\sqrt{5}+\sqrt{6})}{(\sqrt{5}-\sqrt{6})(\sqrt{5}+\sqrt{6})}[/tex]
The denominator is now difference of two squares;
[tex]\frac{11(\sqrt{5}+\sqrt{6})}{(\sqrt{5})^2-(\sqrt{6})^2}[/tex]
Simplify:
[tex]\frac{11(\sqrt{5}+\sqrt{6})}{5-6}[/tex]
[tex]\frac{11(\sqrt{5}+\sqrt{6})}{-1}[/tex]
[tex]-11(\sqrt{5}+\sqrt{6})[/tex]
[tex]-11\sqrt{5}-11\sqrt{6}[/tex]
