Answer:
Second Option
[tex]\frac{5\sqrt{11} +5\sqrt{3}}{8}[/tex]
Step-by-step explanation:
To simplify the expression you must multiply the numerator and the denominator of the fraction by the conjugate of the denominator.
If you have an expression of the form
[tex]a -b[/tex] then its conjugate will be [tex]a + b.[/tex]
The result of that multiplication will be
[tex]a ^ 2 -b ^ 2[/tex]
Therefore we have the expression
[tex]\frac{5}{\sqrt{11} -\sqrt{3}}[/tex]
By multiplying by the conjugate of the denominator we have
[tex]\frac{5}{\sqrt{11} -\sqrt{3}}*\frac{\sqrt{11} +\sqrt{3}}{\sqrt{11} +\sqrt{3}}\\\\\\\frac{5(\sqrt{11} +\sqrt{3})}{(\sqrt{11})^2 -(\sqrt{3})^2}\\\\\\\frac{5\sqrt{11} +5\sqrt{3}}{11 -3}\\\\\\\frac{5\sqrt{11} +5\sqrt{3}}{8}[/tex]
