Answer
$\{\frac{-11\pm\sqrt {85}}{6},\frac{11\pm\sqrt {85}}{6} \}$
Work Step by Step
Step 1. Rewrite the equation as $|\frac{x^2+1}{x}|=\frac{11}{3}$. Remove the absolute value sign to get $\frac{x^2+1}{x}=\frac{11}{3}$ and $\frac{x^2+1}{x}=-\frac{11}{3}$
Step 2. For $\frac{x^2+1}{x}=\frac{11}{3}$, we have $3x^2-11x+3=0$ which gives $x=\frac{11\pm\sqrt {11^2-4(3)(3)}}{2(3)}=\frac{11\pm\sqrt {85}}{6}$
Step 3. For $\frac{x^2+1}{x}=-\frac{11}{3}$, we have $3x^2+11x+3=0$ which gives $x=\frac{-11\pm\sqrt {11^2-4(3)(3)}}{2(3)}=\frac{-11\pm\sqrt {85}}{6}$
Step 4. Combine the above results, we have the solutions as $\{\frac{-11\pm\sqrt {85}}{6},\frac{11\pm\sqrt {85}}{6} \}$
