Simplify the algebraic expression. \( \frac{x^{2} y-x y^{2}+y^{3}}{\frac{x^{2}}{y}+\frac{y^{2}}{x}} \) \( \frac{x^{2} y-x y^{2}+y^{3}}{x^{2}}=\square \)

To simplify the given algebraic expression, let's start with the numerator and denominator separately. The numerator is \( x^2 y - x y^2 + y^3 \). We can factor it: \[ x^2 y - x y^2 + y^3 = y(x^2 - xy) + y^3 = y(x^2 - xy + y^2). \] Now, the denominator \( \frac{x^2}{y} + \frac{y^2}{x} \) can be obtained by finding a common denominator: \[ \frac{x^2}{y} + \frac{y^2}{x} = \frac{x^3 + y^3}{xy}. \] So our expression becomes: \[ \frac{y(x^2 - xy + y^2)}{\frac{x^3 + y^3}{xy}} = \frac{y(x^2 - xy + y^2) \cdot xy}{x^3 + y^3}. \] Now, we can simplify this: \[ \frac{y^2(x^2 - xy + y^2)}{x^3 + y^3}. \] Thus, when written in the format requested, \[ \frac{x^{2} y-x y^{2}+y^{3}}{x^{2}}= \frac{y^2(x^2 - xy + y^2)}{x^3 + y^3} = \square. \]