Decimal into fraction

$$x = 9 + 4\sqrt{5}$$. So, $$\frac{1}{x}$$ = $$9 - 4\sqrt{5}$$. So, $$x+ \frac{1}{x}$$ = 18

$$\frac{1}{3-2\sqrt{2}}-\frac{1}{3+2\sqrt{2}} = \frac{3+2\sqrt{2}-3+2\sqrt{2}}{3^2-(2\sqrt{2})^2} = 4\sqrt{2}/1 = 2^{5/2}$$. Hence x=5/2.

$$\frac{30-\sqrt{884}}{\sqrt{17}+\sqrt{13}} = \frac{(\sqrt{17}-\sqrt{13})^2}{\sqrt{17}+\sqrt{13}} = \frac{(\sqrt{17}-\sqrt{13})^3}{(\sqrt{17}+\sqrt{13})(\sqrt{17}-\sqrt{13})}=\frac{x^3}{17-13} = \frac{x^3}{4}$$.