Divide $\frac{\left(2+\frac{2+\frac{1}{2}}{2-\frac{1}{2}}\right)\cdot 3^{-1}}{2^{-1}}$

$\frac{186\frac{1681}{625}\cdot \frac{1}{2}}{\frac{1}{20}\cdot \frac{1}{20}\cdot \left(186-1\right)+\frac{1681}{625}\cdot \frac{1}{2}}$

$\frac{186\frac{1681}{625}\cdot \frac{1}{2}}{186-1+\frac{1681}{625}\cdot \frac{1}{2}}$

$\frac{6}{2\left(2+1\right)}$

$\frac{23^{\frac{1}{2}}}{33^{\frac{1}{2}}-6^{\frac{1}{2}}}$

$\frac{\left(8\right)\left(-1\right)}{\left(-11^2+4\right)^2}$

$\frac{2\sqrt{3}-\sqrt{2}}{\sqrt{18}}$

$\frac{2+\sqrt{3}}{2-\sqrt{3}}$