Question

Answer of image.....​

Answer 1

Answer:

$-8\sqrt{5}$

Step-by-step explanation:

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

Rationalizing Denominators of both terms,

and using identity -> $a^{2} - b^{2} = (a+b)*(a-b)$

$\frac{(\sqrt{5}-2)*(\sqrt{5} -2) }{(\sqrt{5}+2)*(\sqrt{5} -2) } - \frac{(\sqrt{5}+2)*(\sqrt{5} +2) }{(\sqrt{5}-2)*(\sqrt{5}+2) } \\ \frac{(\sqrt{5}-2) ^{2} }{(\sqrt{5})^{2} - (2)^{2} } -\frac{(\sqrt{5}+2) ^{2} }{(\sqrt{5})^{2} - (2)^{2} }\\\frac{(\sqrt{5} -2)^{2} }{5-4} - \frac{(\sqrt{5}+2)^{2} }{5-4} \\\frac{(\sqrt{5}-2)^{2} - (\sqrt{5}+2)^{2} }{1} \\(\sqrt{5} -2 +\sqrt{5} +2)*(\sqrt{5} -2 - \sqrt{5} -2)\\(2\sqrt{5} )*(-4)\\= -8\sqrt{5}$

Hope this helps!!!

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