Question

Simplify (root 5 - 2 / root 5 + 2) - (root 5 + 2 / root 5 - 2) please give this answer at the earliest.

Answer 1

Answer:

$-8\sqrt{5}$

Step-by-step explanation:

 $(\frac{\sqrt{5} -2}{\sqrt{5} +2})-(\frac{\sqrt{5} +2}{\sqrt{5} -2})$

=$\frac{(\sqrt{5}-2)^{2}-(\sqrt{5}+2)^{2}}{(\sqrt{5}+2)(\sqrt{5}-2)}$

=$\frac{[(\sqrt{5}-2)+(\sqrt{5}+2)][(\sqrt{5}-2)-(\sqrt{5}+2)]}{(\sqrt{5})^{2}-(2)^{2} }$

=$\frac{(2\sqrt{5})(-4)}{5-4}$

=$-8\sqrt{5}/1$

=$-8\sqrt{5}$

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