Answer:
The correct option is b) [tex]\frac{5\sqrt{11}+5\sqrt{3}}{8}[/tex]
Step-by-step explanation:
We need to find the quotient of [tex]\frac{5}{\sqrt{11}-\sqrt{3}}[/tex],
Rationalizing the above,
By multiply and divide by conjugate of its denominator,
[tex]\frac{5}{\sqrt{11}-\sqrt{3}} \times \frac{\sqrt{11}+\sqrt{3}}{\sqrt{11}+\sqrt{3}}[/tex]
[tex]\frac{5(\sqrt{11}+\sqrt{3})}{(\sqrt{11}-\sqrt{3})(\sqrt{11}+\sqrt{3})}[/tex]
Since, [tex](a+b)(a-b)=a^{2}-b^{2}[/tex]
[tex]\frac{5\sqrt{11}+5\sqrt{3}}{(11-3)}[/tex]
simplify,
[tex]\frac{5\sqrt{11}+5\sqrt{3}}{8}[/tex]
Therefore, the correct option is b) [tex]\frac{5\sqrt{11}+5\sqrt{3}}{8}[/tex]
