Question

розв'яжіть рівняння:

Answer 1

$\frac{x - 7}{x - 2} + \frac{x + 4}{x + 2} = 1 \\ \frac{x - 7}{x - 2} + \frac{x + 4}{x + 2} - 1 = 0 \\ \frac{(x + 2) \times (x - 7) + (x - 2) \times (x + 4) - (x - 2) \times (x + 2)}{(x - 2) \times (x + 2)} = 0 \\ \frac{ {x}^{2} - 7x + 2x - 14 + {x}^{2} + 4x - 2x - 8 - ( {x}^{2} - 4) }{(x - 2) \times (x + 2)} = 0 \\ \frac{ {x}^{2} - 7x - 14 + {x}^{2} + 4x - 8 - {x}^{2} + 4 }{(x - 2) \times (x + 2)} = 0 \\ \frac{ - 3x - 18 + {x}^{2} }{(x - 2) \times (x + 2)} = 0 \\ - 3x - 18 + {x}^{2} = 0 \\ {x}^{2} - 3x - 18 = 0 \\ {x}^{2} + 3x - 6x - 18 = 0 \\ x(x + 3) - 6(x + 3) = 0 \\ (x + 3) \times (x - 6) = 0 \\ x + 3 = 0 \\ x - 6 = 0 \\ x = - 3 \\ x = 6 \\ \\ x_{1} = - 3 . x_{2} = 6$