![\frac{x(3-x)}{x+4}\geq0 \frac{x(3-x)}{x+4}\geq0](https://tex.z-dn.net/?f=%5Cfrac%7Bx%283-x%29%7D%7Bx%2B4%7D%5Cgeq0)
ОДЗ (Область допустимых значений): x ≠ -4
1 способ:
![\frac{3x-x^{2})}{x+4}\geq0 \frac{3x-x^{2})}{x+4}\geq0](https://tex.z-dn.net/?f=%5Cfrac%7B3x-x%5E%7B2%7D%29%7D%7Bx%2B4%7D%5Cgeq0)
0}} \right. \\\left \{ {{x(3-x)\leq0} \atop {x+4<0}} \right." alt="\left \{ {{x(3-x)\geq0} \atop {x+4>0}} \right. \\\left \{ {{x(3-x)\leq0} \atop {x+4<0}} \right." align="absmiddle" class="latex-formula">
-4}} \right. \\\left \{ {{x\in(-\infty;0]\cup[3;+\infty)} \atop {x<-4}} \right." alt="\left \{ {{x\in[0,3]} \atop {x>-4}} \right. \\\left \{ {{x\in(-\infty;0]\cup[3;+\infty)} \atop {x<-4}} \right." align="absmiddle" class="latex-formula">
![x\in[0,3]\\x\in(-\infty,-4) x\in[0,3]\\x\in(-\infty,-4)](https://tex.z-dn.net/?f=x%5Cin%5B0%2C3%5D%5C%5Cx%5Cin%28-%5Cinfty%2C-4%29)
Учитывая ОДЗ, окончательный ответ:
![x\in(-\infty,-4)\cup[0,3] x\in(-\infty,-4)\cup[0,3]](https://tex.z-dn.net/?f=x%5Cin%28-%5Cinfty%2C-4%29%5Ccup%5B0%2C3%5D)
2 способ:
![x(3-x)=0 x(3-x)=0](https://tex.z-dn.net/?f=x%283-x%29%3D0)
![x_{1}=0; x_{2}=3 x_{1}=0; x_{2}=3](https://tex.z-dn.net/?f=x_%7B1%7D%3D0%3B%20x_%7B2%7D%3D3)
Дальше см. изображение
Ответ: ![x\in(-\infty,-4)\cup[0,3] x\in(-\infty,-4)\cup[0,3]](https://tex.z-dn.net/?f=x%5Cin%28-%5Cinfty%2C-4%29%5Ccup%5B0%2C3%5D)