$x^{2} y\left(\frac{1}{x^{2}}+\frac{2}{x y}\right)$
\(\boxed{2x + y}\) is the final simplified expression.
Step 1 :Simplify the given expression: $x^{2} y\left(\frac{1}{x^{2}}+\frac{2}{x y}\right)$
Step 2 :Combine the terms inside the parentheses: $x^{2} y\left(x^{-2}+\frac{2}{x y}\right)$
Step 3 :Distribute $x^{2}y$ to the terms inside the parentheses: $x^{2}y(x^{-2}) + x^{2}y\left(\frac{2}{x y}\right)$
Step 4 :Simplify the terms: $y + 2x$
Step 5 :\(\boxed{2x + y}\) is the final simplified expression.