Simplify the following 7-3 7+3 - 7+3 7-3 - Vidyadip

Question

Simplify the following$\frac{\sqrt{7}-\sqrt{3}}{\sqrt{7}+\sqrt{3}}-\frac{\sqrt{7}+\sqrt{3}}{\sqrt{7}-\sqrt{3}}$

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Answer

$\frac{\sqrt{7}-\sqrt{3}}{\sqrt{7}+\sqrt{3}}-\frac{\sqrt{7}+\sqrt{3}}{\sqrt{7}-\sqrt{3}} $
$ =\frac{(\sqrt{7}-\sqrt{3})^2-(\sqrt{7}+\sqrt{3})^2}{(\sqrt{7}+\sqrt{3})(\sqrt{7}-\sqrt{3})} $
$ =\frac{7+3-2 \sqrt{21}-7-3-2 \sqrt{21}}{(\sqrt{7})^2-(\sqrt{3})^2} $
$ =\frac{-4 \sqrt{21}}{7-3} $
$ =-\sqrt{21}$

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