Question

задание на упрощение выражения

Answer 1

(-x^2-3x-2)^2/x^2+4x+4-2x^2-x-1/x-1=x^4+9x^2+4/x^2+4x+4-2x^2-x-1/x-1=x^2+9x^2+4-8x^2-4x-4/4x-4=2x^2-4x/4x-4=2x^2/4

Answer 2

$frac{(-x^{2}-3x-2)}{x^{2}+4x+4}-frac{2x^{2}-x-1}{x-1}\\ 1. -x^{2}-3x-2=0\ D = b^{2}-4ac=(-3)^{2}-4cdot (-1)cdot (-2)=9-8=1\ x_{1,2}=frac{-b+/-sqrt{D}}{2a}\ x_{1}=frac{3+1}{2cdot (-1)}=frac{4}{-2}=-2\ x_{2}=frac{3-1}{2cdot (-1)}=frac{2}{-2}=-1\ -x^{2}-3x-2=-(x+1)(x+2)\\ 2. x^{2}+4x+4= (x+2)^{2}\\ 3. 2x^{2}-x-1=0\ a+b+c = 0 => x_{1}=1, x_{2}=frac{c}{a}\ 2+(-1)+(-1)=0\ x_{1}=1, x_{2}=frac{-1}{2}=-frac{1}{2}\ 2x^{2}-x-1=2(x-1)(x+frac{1}{2})$

$frac{-(x+1)(x+2)}{(x+2)^{2}}-frac{2(x-1)(x+frac{1}{2})}{x-1}=-frac{(x+1)(x+2)}{(x+2)^{2}}-frac{2(x-1)(x+frac{1}{2})}{x-1}=\ =-frac{x+1}{x+2}-2(x+frac{1}{2}}) | cdot (x+2)=-(x+1)-2(x+frac{1}{2})(x+2)=\ =-x-1-2(x^{2}+2x+frac{1}{2}x+1)=-x-1-2(x^{2}+frac{5}{2}+1)=\ =-x-1-2x^{2}-5x-2=-2x^{2}-6x-3\\ -2x^{2}-6x-3=0\ D = (-6)^{2}-4cdot (-2)cdot (-3)=36-24=12\ x_{1}=frac{6+sqrt{12}}{-4}=-frac{6+2sqrt{3}}{4}=-frac{2(3+sqrt{3})}{4}=-frac{3+sqrt{3}}{2}$

$x_{2}=frac{6-sqrt{12}}{-4}=-frac{6-2sqrt{3}}{4}=-frac{2(3-sqrt{3})}{4}=-frac{3-sqrt{3}}{2}\\ -2x^{2}-6x-3=-2(x+frac{3+sqrt{3}}{2})(x+frac{3-sqrt{3}}{2})$