$((\frac{32}{57} + \frac{27}{38}) * \frac{19}{29} + (\frac{25}{26} + \frac{48}{65}) * \frac{10}{51} + (\frac{74}{75} + \frac{49}{50}) * \frac{15}{59}) * \frac{3}{5} = (\frac{32 * 2 + 27 * 3}{114} * \frac{19}{29} + \frac{25 * 5 + 48 * 2}{130} * \frac{10}{51} + \frac{74 * 2 + 49 * 3}{150} * \frac{15}{59}) * \frac{3}{5} = (\frac{64 + 81}{114} * \frac{19}{29} + \frac{125 + 96}{130} * \frac{10}{51} + \frac{148 + 147}{150} * \frac{15}{59}) * \frac{3}{5} = (\frac{145}{114} * \frac{19}{29} + \frac{221}{130} * \frac{10}{51} + \frac{295}{150} * \frac{15}{59}) * \frac{3}{5} = \frac{145}{114} * \frac{19}{29} * \frac{3}{5} + \frac{221}{130} * \frac{10}{51} * \frac{3}{5} + \frac{295}{150} * \frac{15}{59} * \frac{3}{5} = \frac{29 * 5}{19 * 2 * 3} * \frac{19}{29} * \frac{3}{5} + \frac{13 * 17}{13 * 5 * 2} * \frac{2 * 5}{17 * 3} * \frac{3}{5} + \frac{5 * 59}{10 * 5 * 3} * \frac{5 * 3}{59} * \frac{3}{5} = \frac{1}{2} + \frac{1}{5} + \frac{3}{10} = \frac{1 * 5 + 1 * 2 + 3}{10} = \frac{5 + 2 + 3}{10} = \frac{10}{10} = 1$