Solve the following equations: 1) \(\frac{x - 0.7}{x + 0.3} = \frac{5.7}{4.7}\) 2) \(\frac{19.5}{x - 2.4} = \frac{47.25}{x + 1.3}\)

Пошаговое решение:

1. Уравнение 1:
   \( \frac{x - 0.7}{x + 0.3} = \frac{5.7}{4.7} \)
   \( 4.7(x - 0.7) = 5.7(x + 0.3) \)
   \( 4.7x - 3.279 = 5.7x + 1.71 \)
   \( 4.7x - 5.7x = 1.71 + 3.279 \)
   \( -1.0x = 4.989 \)
   \( x = -4.989 \)
2. Уравнение 2:
   \( \frac{19.5}{x - 2.4} = \frac{47.25}{x + 1.3} \)
   \( 19.5(x + 1.3) = 47.25(x - 2.4) \)
   \( 19.5x + 25.35 = 47.25x - 113.4 \)
   \( 19.5x - 47.25x = -113.4 - 25.35 \)
   \( -27.75x = -138.75 \)
   \( x = \frac{-138.75}{-27.75} \)
   \( x = 4.99 \)

Ответ: 1) x = -4.989; 2) x = 4.99