Step 1 :The given mathematical expression is \(\frac{18 x^{3} y^{2}+9 x^{2} y^{5}}{3 x^{3} y^{2}}\).
Step 2 :To simplify this expression, we can divide each term in the numerator by the denominator. This will simplify the expression by reducing the powers of x and y in each term.
Step 3 :The simplified expression is \(6 + \frac{3y^{3}}{x}\).
Step 4 :Final Answer: The simplified form of the given expression is \(\boxed{6 + \frac{3y^{3}}{x}}\).