[tex] a= 0,(6) + \sqrt6 \cdot \dfrac{3}{4} \\ \\ a = \dfrac{6}{9} + \dfrac{3\sqrt6}{4} \\ \\ a = \dfrac{2}{3} + \dfrac{3\sqrt6}{4} \\ \\ a = \dfrac{2\cdot4 + 3\sqrt6 \cdot 3}{12} \\ \\ a = \dfrac{8+9\sqrt6}{12} \Big| \cdot 3 \\ \\ 3a = \dfrac{8+9\sqrt6}{4} \Big|-2 \\ \\ 3a-2 = \dfrac{8+9\sqrt6}{4} -2 \Big|\cdot4 \\ \\ 4\cdot(3a-2) = 8+9\sqrt6 - 8 \\ \\ 4\cdot(3a-2) = 9\sqrt6[/tex]
