Question

root 5 minus 2 upon root 5 + 2 minus root 5 + 2 upon root 5 minus 2

Answer 1

-8√5 is the answer to this question

Answer 2

Answer:

The value of given expression is $-8\sqrt{5}$.

Step-by-step explanation:

The given expression is

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

Rationalize the denominator.

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

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

$5-4\sqrt{5}-(5+4\sqrt{5})$

$5-4\sqrt{5}-5-4\sqrt{5}$

$-8\sqrt{5}$

Therefore the value of given expression is $-8\sqrt{5}$.