[tex] \frac{2}{3} *( \frac{1}{3} + \frac{1}{1/2} - \frac{1}{3/2} ) = \frac{2}{3} *( \frac{1}{3} + \frac{1}{1/2} - \frac{2}{3} ) \\ \\ = \frac{2}{3} *( \frac{1}{3} + 2 - \frac{2}{3} ) = \frac{2}{3}*( 2-\frac{1}{3} ) = \frac{2}{3}*( \frac{5}{3} ) \\ \\ \frac{1}{2/3} - \frac{1}{5/3} + \frac{1}{10/9} \\ \\ = \frac{3}{2} - \frac{3}{5} + \frac{9}{10} = \frac{18}{10} = \frac{9}{5} [/tex]
