Question

Simplify root 5 - 2 / root 5 + 2 - root 5 + 2 / root 5 - 2

Answer 1

Step-by-step explanation:

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}.