Решить систему :360/y - 360/x = 2360/y+30 - 360/x+30 = 1

[latex]\frac{360}{y}-\frac{360}{x}=2\\ \frac{360}{y+30}-\frac{360}{x+30}=1\\\\ \frac{360x-360y}{xy}=2\\ \frac{360(x+30)- 360(y+30)}{(y+30)(x+30)}=1\\ \\ \frac{360x-360y}{yx+30y+30x+900}=1\\ \frac{360x-360y}{xy}=2\\\\ \\ 360x-360y=yx+30(y+x)+900\\ 360x -360y=2yx\\ \\ yx+30(y+x)+900=2yx\\ 30(y+x)+900=yx 30y+30x+900=yx\\ 30y-yx=-30x-900\\ y(30-x)=-30x-900\\ y=\frac{-30x-900}{30-x}\\ y=\frac{-30x-900}{30-x}\\ \frac{360(30-x)}{-30x-900}-\frac{360}{x}=2\\ x^2-78x-1080=0\\ D=\sqrt{10404}\\ x_{1}=90\\ x_{2}=-12\\ [/latex] [latex]y_{1}=-12\frac{6}{7}\\ y_{2}=60[/latex]