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