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

We start with the expression \[ \frac{x^{2}-2xy+y^{2}}{\frac{x}{y}-\frac{y}{x}}. \] 1. **Factor the numerator:** Notice that \[ x^{2}-2xy+y^{2} = (x-y)^2. \] 2. **Combine the denominator into a single fraction:** Write \[ \frac{x}{y}-\frac{y}{x} = \frac{x^2 - y^2}{xy}. \] We also recognize that \[ x^2 - y^2 = (x-y)(x+y). \] So, the denominator becomes \[ \frac{(x-y)(x+y)}{xy}. \] 3. **Rewrite the original expression:** Substitute the factorizations into the expression: \[ \frac{(x-y)^2}{\frac{(x-y)(x+y)}{xy}}. \] 4. **Simplify by multiplying by the reciprocal:** Multiply by the reciprocal of the denominator: \[ \frac{(x-y)^2 \cdot xy}{(x-y)(x+y)}. \] 5. **Cancel the common factor:** Cancel one factor of \((x-y)\) from the numerator and denominator (assuming \(x \neq y\)): \[ \frac{xy(x-y)}{x+y}. \] Thus, the simplified expression is \[ \frac{xy(x-y)}{x+y}. \]