Answer
$\frac{y(3x+2y)}{y^2+2x}$.
Work Step by Step
The given expression is
$=\frac{\frac{3}{xy^2}+\frac{2}{x^2y}}{\frac{1}{x^2y}+\frac{2}{xy^3}}$
Multiply the numerator and the denominator by $x^2y^3$.
$=\frac{x^2y^3}{x^2y^3}\cdot \frac{\frac{2}{x^3y}+\frac{5}{xy^4}}{\frac{5}{x^3y}-\frac{3}{xy}}$
Use the distributive property.
$=\frac{x^2y^3\cdot \frac{3}{xy^2}+x^2y^3\cdot \frac{2}{x^2y}}{x^2y^3\cdot \frac{1}{x^2y}+x^2y^3\cdot \frac{2}{xy^3}}$
Simplify.
$=\frac{3xy+2y^2}{y^2+2x}$
Factor out common terms in the numerator.
$=\frac{y(3x+2y)}{y^2+2x}$.
