Question

скоротіть дріб:
$\frac{ {x}^{2} - 10x + 24}{ {x}^{2} - 4}$
$\frac{ {x}^{2} + 11x + 30}{ {x}^{2} + 5x }$

Answer 1

$a) \frac{ {x}^{2} - 10x + 24}{ {x}^{2} - 4} = \frac{(x-4)(x-6)}{(x-4)(x+4)} = \frac{x-6}{x+4} \\ x^2-10x+24=(x-4)(x-6) \\ \left \{ {{x_1*x_2=24} \atop {x_1+x_2=10}} \right. \left \{ {{x_1=4} \atop {x_2=6}} \right. \\ \\ \\ b) \frac{ {x}^{2} + 11x + 30}{ {x}^{2} + 5x } = \frac{(x+6)(x+5)}{x(x+5)} = \frac{x+6}{x} \\ x^2+11x+30=(x+6)(x+5) \\ \left \{ {{x_1*x_2=30} \atop {x_1+x_2=-11}} \right. \left \{ {{x_1=-6} \atop {x_2=-5}} \right.$