2.212 Найдите корень уравнения: д) $$5\frac{25}{36} - t = 1\frac{1}{12} + 2\frac{3}{8}$$;

Выразим $$t$$:

$$t = 5\frac{25}{36} - (1\frac{1}{12} + 2\frac{3}{8})$$

1. $$1\frac{1}{12} + 2\frac{3}{8} = \frac{13}{12} + \frac{19}{8} = \frac{13 \cdot 2}{12 \cdot 2} + \frac{19 \cdot 3}{8 \cdot 3} = \frac{26}{24} + \frac{57}{24} = \frac{83}{24}$$

$$t = 5\frac{25}{36} - \frac{83}{24} = \frac{205}{36} - \frac{83}{24} = \frac{205 \cdot 2}{36 \cdot 2} - \frac{83 \cdot 3}{24 \cdot 3} = \frac{410}{72} - \frac{249}{72} = \frac{161}{72} = 2\frac{17}{72}$$

Ответ: $$t = 2\frac{17}{72}$$