Question

3. Решите уравнение = х/+4=3/x-1
4. Сократите дробь х²-3х/2х²-8х+6
5. Решите уравнение |3х²+7х|-6=0​

Answer 1

$\displaystyle 1)\frac{x}{x+4}=\frac{3}{x-1},x\neq -4,x\neq 1\\\\x(x-1)=3(x+4)\\x(x-1)-3(x+4)=0\\x^2-x-3x-12=0\\x^2-4x-12=0\\x^2+2x-6x-12=0\\x(x+2)-6(x+2)=0\\(x+2)(x-6)=0\\x+2=0,x-6=0\\x_1=-2,x_2=6\\\\2) \frac{x^2-3x}{2x^2-8x+6}=\frac{x(x-3)}{2(x^2-4x+3)}=\frac{x(x-3)}{2(x^2-x-3x+3)}=\frac{x(x-3)}{2(x(x-1)-3(x-1))}=\frac{x(x-3)}{2(x-1)(x-3)}=\frac{x}{2(x-1)}=\frac{x}{2x-2}\\\\3)|3x^2+7x|-6=0\\|3x^2+7x|=6\\3x^2+7x=6,3x^2+7x=-6\\\\x_1=-3,x_2=\frac{2}{3}$