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

To simplify the algebraic expression: \[ \frac{x^{2} - 2xy + y^{2}}{\frac{x}{y} - \frac{y}{x}} \] **Step 1: Factor the Numerator and Denominator** 1. **Numerator:** \(x^{2} - 2xy + y^{2}\) can be factored as: \[ (x - y)^2 \] 2. **Denominator:** \(\frac{x}{y} - \frac{y}{x}\) can be rewritten with a common denominator: \[ \frac{x^2 - y^2}{xy} = \frac{(x - y)(x + y)}{xy} \] **Step 2: Rewrite the Expression** Substitute the factored forms back into the original expression: \[ \frac{(x - y)^2}{\frac{(x - y)(x + y)}{xy}} = (x - y)^2 \times \frac{xy}{(x - y)(x + y)} \] **Step 3: Simplify by Canceling Common Terms** Cancel out one \((x - y)\) from the numerator and denominator: \[ (x - y) \times \frac{xy}{x + y} = \frac{xy(x - y)}{x + y} \] **Final Simplified Expression:** \[ \frac{xy(x - y)}{x + y} \] **Answer:** \[ \frac{xy(x - y)}{\,x + y\,} \]