Question

Помогите пожалуйста. Решение дробно рациональных уравнений.

Answer 1

$\frac{x - 3}{2x - 1} = \frac{x - 9}{x} \\ \\ x \times (x - 3) = (x - 9) \times (2x - 1) \\ \\ x {}^{2} - 3x - 2x {}^{2} + 19x - 9 = 0 \\ \\ - x {}^{2} + 16x - 9 = 0 \\ \\ x {}^{2} - 16x + 9 = 0$

D = ( -16 )² - 4 * 1 * 9 = 256 - 36 = 220

$x1 = \frac{16 - \sqrt{220} }{2} \\ \\ x2 = \frac{16 + \sqrt{220} }{2} \\ \\ x1 = 8 - \sqrt{55} \\ \\ x2 = 8 + \sqrt{55} \\ \\ \\ \\ 2) \frac{x - 2}{2} + \frac{2x}{3} = \frac{5x}{6} \\ \\ 3 \times (x - 2) + 4x = 5x \\ \\ 3x - 6 + 4x = 5x \\ \\ 7x - 5x = 6 \\ \\ 2x = 6 \\ \\ x = \frac{6}{2} \\ \\ x = 3 \\ \\ \\ 3)4x + 3 = 6 \times (5 - x) \\ \\ 4x + 3 = 30 - 6x \\ \\ 4x + 6x = 30 - 3 \\ \\ 10x = 27 \\ \\ x = \frac{27}{10} \\ \\ x = 2.7 \\ \\ \\ \\ 4) \frac{8}{x} = 3x - 2 \\ \\ 8 = x \times (3x - 2) \\ \\ 8 - 3x {}^{2} + 2x = 0 \\ \\ - 3x {}^{2} + 2x + 8 = 0 \\ \\ 3x {}^{2} - 2x - 8 = 0$

D = ( -2 )² - 4 * 3 * ( -8 ) = 4 + 96 = 100

$x1 = \frac{2 - 10}{2 \times 3} \\ \\ x2 = \frac{2 + 10}{2 \times 3} \\ \\ x1 = - \frac{4}{3} \\ \\ x2 = 2$

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