Rationalize the denominator $\frac{\left(\frac{4\sqrt{3}-2\sqrt{5}+\sqrt{2}}{2\sqrt{6}}\right)\cdot 2\sqrt{6}}{2\sqrt{6}}$

$\frac{4}{\frac{t-4}{3\left(\sqrt{t}-2\right)}}$

$\frac{1}{\sqrt{3}}$

$\frac{4}{\sqrt{5}-1}$

$\frac{a^{121\left(-1\right)} b^{121\left(-1\right)}}{\left(a^{-1} b^{-1}\right)^2}$

$\frac{12}{\sqrt{15}-\sqrt{6}+\sqrt{35}-\sqrt{14}}$

$\frac{1}{\left(aa\cdot a\right)^{\frac{1}{4}}+\sqrt{aa\cdot a}}$

$\frac{1161\left(-1\right)}{x^{2\left(\frac{4\sqrt{x}}{\sqrt{x}}+\frac{4\sqrt{x}}{\sqrt{x}}\right)}}$