\frac{x\cdot2x-x^2-9}{x^2}=0\\(x-3)(x+3)=0\\x=-3\\y(-11)=\frac{121+9}{-11}=-\frac{130}{11}\\y(-1)=\frac{1+9}{-1}=-10\\y(-3)=\frac{9+9}{-3}=-6=y_{max}" alt="y=\frac{x^2+9}{x}\\\\y'=\frac{x\cdot2x-x^2}{x}\\y'=0<=>\frac{x\cdot2x-x^2-9}{x^2}=0\\(x-3)(x+3)=0\\x=-3\\y(-11)=\frac{121+9}{-11}=-\frac{130}{11}\\y(-1)=\frac{1+9}{-1}=-10\\y(-3)=\frac{9+9}{-3}=-6=y_{max}" align="absmiddle" class="latex-formula">