Question

Скоротіть дріб (x² -7x+12)/(x²+x-20) с объяснением пожалуйста (80 балов)

Answer 1

По теореме Виета:

${x}^{2} + bx + c = 0\\ x_{1} + x_{2} = - b\\ x_{1} x_{2} = c$

${x}^{2} - 7x + 1 2 = 0 \\ x_{1} + x_{2} = 7 \\ x_{1} x_{2} = 12 \\ x_{1} = 3\\ x_{2} = 4 \\ {ax}^{2} + bx + c = a(x - x_{1})(x - x_{2})\\ {x}^{2} - 7x + 12 = (x - 3)(x - 4)$

${x}^{2} + x - 20 = 0 \\ x_{1} + x_{2} = - 1 \\ x_{1} x_{2} = - 20 \\ x_{1} = - 5\\ x_{2} =4 \\{ax}^{2} + bx + c = a(x - x_{1})(x - x_{2}) \\ {x}^{2} + x - 20 = (x + 5)(x - 4)$

$\frac{ {x}^{2} - 7x + 12}{ {x}^{2} + x - 20 } = \frac{(x - 3)(x - 4)}{(x + 5)(x - 4)} = \frac{x - 3}{x + 5}$