Question
Simplify the following$\frac{\sqrt{5}-2}{\sqrt{5}+2}-\frac{\sqrt{5}+2}{\sqrt{5}-2}$
✓
Answer
$\frac{\sqrt{5}-2}{\sqrt{5}+2}-\frac{\sqrt{5}+2}{\sqrt{5}-2}$
$ =\frac{(\sqrt{5}-2)^2-(\sqrt{5}+2)^2}{(\sqrt{5}+2)(\sqrt{5}-2)}$
$ =\frac{5+4-4 \sqrt{5}-5-4-4 \sqrt{5}}{(\sqrt{5})^2-(2)^2} $
$=\frac{-8 \sqrt{5}}{5-4}$
$ =-8 \sqrt{5}$
$ =\frac{(\sqrt{5}-2)^2-(\sqrt{5}+2)^2}{(\sqrt{5}+2)(\sqrt{5}-2)}$
$ =\frac{5+4-4 \sqrt{5}-5-4-4 \sqrt{5}}{(\sqrt{5})^2-(2)^2} $
$=\frac{-8 \sqrt{5}}{5-4}$
$ =-8 \sqrt{5}$
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