Write the Fraction in Simplest Form 1/(2+ square root of 5)

$\frac{1}{2 + \sqrt{5}}$

Multiply $\frac{1}{2 + \sqrt{5}}$ by $\frac{2 - \sqrt{5}}{2 - \sqrt{5}}$ .

$\frac{1}{2 + \sqrt{5}} \cdot \frac{2 - \sqrt{5}}{2 - \sqrt{5}}$

Multiply $\frac{1}{2 + \sqrt{5}}$ by $\frac{2 - \sqrt{5}}{2 - \sqrt{5}}$ .

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

Expand the denominator using the FOIL method.

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

Simplify.

$\frac{2 - \sqrt{5}}{- 1}$

Move the negative one from the denominator of $\frac{2 - \sqrt{5}}{- 1}$ .

$- 1 \cdot (2 - \sqrt{5})$

Rewrite $- 1 \cdot (2 - \sqrt{5})$ as $- (2 - \sqrt{5})$ .

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

Apply the distributive property.

$- 1 \cdot 2 - - \sqrt{5}$

Multiply $- 1$ by $2$ .

$- 2 - - \sqrt{5}$

Multiply $- - \sqrt{5}$ .

Multiply $- 1$ by $- 1$ .

$- 2 + 1 \sqrt{5}$

Multiply $\sqrt{5}$ by $1$ .

$- 2 + \sqrt{5}$