what is the following quotient?\n$\frac{2}{sqrt{13}+sqrt{11}}$\n$sqrt{13}-2sqrt{11}$\n$\frac{sqrt{13}+sqrt{11…

Explanation:

Step1: Rationalize the denominator

Multiply the numerator and denominator by $\sqrt{13}-\sqrt{11}$. $\frac{2}{\sqrt{13}+\sqrt{11}}\times\frac{\sqrt{13}-\sqrt{11}}{\sqrt{13}-\sqrt{11}}$

Step2: Expand the denominator using difference - of - squares

$(a + b)(a - b)=a^{2}-b^{2}$. Here $a=\sqrt{13}$ and $b = \sqrt{11}$, so the denominator is $(\sqrt{13})^{2}-(\sqrt{11})^{2}=13 - 11=2$. The numerator is $2(\sqrt{13}-\sqrt{11})$.

Step3: Simplify the fraction

$\frac{2(\sqrt{13}-\sqrt{11})}{2}=\sqrt{13}-\sqrt{11}$

Answer:

$\sqrt{13}-\sqrt{11}$