Answer
See explanations.
Work Step by Step
Method 1. Evaluate the numerator and the denominator separately:
$\frac{3}{x}+\frac{2}{x^2}=\frac{3x+2}{x^2}$ and $\frac{1}{x^2}+\frac{2}{x}=\frac{1+2x}{x^2}$.
Then combine the results with division to get
$\frac{3x+2}{x^2}\div\frac{1+2x}{x^2}=\frac{3x+2}{x^2}\times\frac{x^2}{2x+1}=\frac{3x+2}{2x+1}$
Method 2. Multiply the numerator and the denominator by the least common denominator $LCD=x^2$,
$\frac{\frac{3}{x}+\frac{2}{x^2}}{\frac{1}{x^2}+\frac{2}{x}}\times\frac{x^2}{x^2}=\frac{3x+2}{1+2x}$
