`A = \sqrt{9-4\sqrt{5}} + \frac{1}{\sqrt{5}-2}`
`A = \sqrt{2^2-4\sqrt{5}+(\sqrt{5})^2}+\frac{\sqrt{5}+2}{(\sqrt{5}-2)(\sqrt{5}+2)}`
`A = \sqrt{(2 - \sqrt{5})^2} + \frac{\sqrt{5}+2}{5-4}`
`A = \sqrt{(\sqrt{5}-2)^2} + \sqrt{5}+2`
`A = \sqrt{5} - 2 + \sqrt{5} + 2`
`A = 2\sqrt{5}`