Simplify $\frac{\sqrt{13}-\sqrt{11}}{\sqrt{13}+\sqrt{11}}+\frac{\sqrt{13}+\sqrt{11}}{\sqrt{13}-\sqrt{11}}$.
$\frac{\sqrt{13}-\sqrt{11}}{\sqrt{13}+\sqrt{11}}+\frac{\sqrt{13}+\sqrt{11}}{\sqrt{13}-\sqrt{11}}$
$=\frac{\sqrt{13}-\sqrt{11}}{\sqrt{13}+\sqrt{11}} \times \frac{\sqrt{13}-\sqrt{11}}{\sqrt{13}-\sqrt{11}}+\frac{\sqrt{13}+\sqrt{11}}{\sqrt{13}-\sqrt{11}} \times \frac{\sqrt{13}+\sqrt{11}}{\sqrt{13}+\sqrt{11}}$
$=\frac{(\sqrt{13}-\sqrt{11})^{2}}{(\sqrt{13})^{2}-(\sqrt{11})^{2}}+\frac{(\sqrt{13}+\sqrt{11})^{2}}{(\sqrt{13})^{2}-(\sqrt{11})^{2}}$
$=\frac{13+11-2 \times \sqrt{13} \times \sqrt{11}}{13-11}+\frac{13+11+2 \times \sqrt{13} \times \sqrt{11}}{13-11}$
$=\frac{24-2 \sqrt{143}}{2}+\frac{24+2 \sqrt{143}}{2}$
$=\frac{24-2 \sqrt{143}+24+2 \sqrt{143}}{2}$
$=\frac{48}{2}$
$=24$
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