Question

Сократите дробь
Примеры 4,5,6​

Answer 1

$4)\ \ \dfrac{7x^2-x}{2-13x-7x^2}=\dfrac{x\, (7x-1)}{-7(x-\frac{1}{7})(x+2)}=\dfrac{x\, (7x-1)}{-(7x-1)(x+2)}=-\dfrac{x}{x+2}\\\\\\\star \ 2-13x-7x^2=0\ \ ,\ \ -7x^2-13x+2=0\ ,\ \ D=225\ ,\ x_{1,2}=\dfrac{13\pm 15}{-14}\\\\x_1=\dfrac{1}{7}\ \ ,\ \ x_2=-2\ \ \star$

$5)\ \ \dfrac{2x^2+2x-24}{(6-2x)^2}=\dfrac{2\cdot (x^2+x-12)}{(\, -2\cdot (x-3)\, )^2}=\dfrac{2\cdot (x+4)(x-3)}{4\cdot (x-3)^2}=\dfrac{x+4}{2\cdot (x-3)}\\\\\\\star \ \ x^2+x-12=0\ \ ,\ \ x_1=-4\ ,\ x_2=3\ \ (teorema\ Vieta)\ \ \star$

$6)\ \ \dfrac{9a^2-9a+2}{1-3a+b-3ab}=\dfrac{9\cdot (a-\frac{1}{3})(a-\frac{2}{3})}{(1-3a)+b\, (1-3a)}=\dfrac{(3a-1)(3a-2)}{(1-3a)(1+b)}=\dfrac{2-3a}{1+b}\\\\\\\star \ \ 9a^2-9a+2=0\ \ ,\ \ D=9\ ,\ \ a_1=\dfrac{1}{3}\ \ ,\ \ a_2=\dfrac{12}{18}=\dfrac{2}{3}\ \ \star$