Question

$\frac{\sqrt{11}-\sqrt{7}}{\sqrt{11}+\sqrt{7}}\times \frac{\sqrt{11}-\sqrt{7}}{\sqrt{11}-\sqrt{7}}$

Answer 1

Let

$=\frac{(\sqrt{11}-\sqrt{7}{)}^2}{(\sqrt{11}{)}^2-(\sqrt{7}{)}^2}$

$=\frac{11+7-2\sqrt{11}\sqrt{7}}{11-7}$

$=\frac{18-2\sqrt{77}}{4}$

$=\frac{9-\sqrt{77}}{2}$