$$\frac { 6 + \sqrt { 5 } } { 9 - 2 \sqrt { 5 } } \times \frac { 9 + 2 \sqrt { 5 } } { 9 + 2 \sqrt { 5 } }$$
$\frac{21\sqrt{5}+64}{61}\approx 1.818974222$
$$\frac{6+\sqrt{5}}{9-2\sqrt{5}}\times 1$$
$$\frac{\left(6+\sqrt{5}\right)\left(9+2\sqrt{5}\right)}{\left(9-2\sqrt{5}\right)\left(9+2\sqrt{5}\right)}\times 1$$
$$\frac{\left(6+\sqrt{5}\right)\left(9+2\sqrt{5}\right)}{9^{2}-\left(-2\sqrt{5}\right)^{2}}\times 1$$
$$\frac{\left(6+\sqrt{5}\right)\left(9+2\sqrt{5}\right)}{81-\left(-2\sqrt{5}\right)^{2}}\times 1$$
$$\frac{\left(6+\sqrt{5}\right)\left(9+2\sqrt{5}\right)}{81-\left(-2\right)^{2}\left(\sqrt{5}\right)^{2}}\times 1$$
$$\frac{\left(6+\sqrt{5}\right)\left(9+2\sqrt{5}\right)}{81-4\left(\sqrt{5}\right)^{2}}\times 1$$
$$\frac{\left(6+\sqrt{5}\right)\left(9+2\sqrt{5}\right)}{81-4\times 5}\times 1$$
$$\frac{\left(6+\sqrt{5}\right)\left(9+2\sqrt{5}\right)}{81-20}\times 1$$
$$\frac{\left(6+\sqrt{5}\right)\left(9+2\sqrt{5}\right)}{61}\times 1$$
$$\frac{\left(6+\sqrt{5}\right)\left(9+2\sqrt{5}\right)}{61}$$
$$\frac{54+12\sqrt{5}+9\sqrt{5}+2\left(\sqrt{5}\right)^{2}}{61}$$
$$\frac{54+21\sqrt{5}+2\left(\sqrt{5}\right)^{2}}{61}$$
$$\frac{54+21\sqrt{5}+2\times 5}{61}$$
$$\frac{54+21\sqrt{5}+10}{61}$$
$$\frac{64+21\sqrt{5}}{61}$$
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