Решите уравнение: 15\(\frac{4}{19}\)+x+3\(\frac{17}{19}\)=21\(\frac{2}{19}\)

Решение:

1. Приведем смешанные числа к неправильным дробям:

15\(\frac{4}{19}\) = \(\frac{15 \times 19 + 4}{19}\) = \(\frac{285 + 4}{19}\) = \(\frac{289}{19}\)

3\(\frac{17}{19}\) = \(\frac{3 \times 19 + 17}{19}\) = \(\frac{57 + 17}{19}\) = \(\frac{74}{19}\)

21\(\frac{2}{19}\) = \(\frac{21 \times 19 + 2}{19}\) = \(\frac{399 + 2}{19}\) = \(\frac{401}{19}\)

2. Подставим в уравнение:

\(\frac{289}{19}\) + x + \(\frac{74}{19}\) = \(\frac{401}{19}\)

3. Сложим известные дроби:

\(\frac{289 + 74}{19}\) + x = \(\frac{401}{19}\)

\(\frac{363}{19}\) + x = \(\frac{401}{19}\)

4. Выразим x:

x = \(\frac{401}{19}\) - \(\frac{363}{19}\)

x = \(\frac{401 - 363}{19}\)

x = \(\frac{38}{19}\)

x = 2

Ответ: 2