Chapter 7 - Section 7.5 - Rationalizing Denominators and Numerators of Radical Expressions - Exercise Set - Page 445: 51

$\dfrac{x-\sqrt{xy}}{x-y}$

Rationalizing the denominator of $ \dfrac{\sqrt{x}}{\sqrt{x}+\sqrt{y}} $ results to \begin{array}{l} \dfrac{\sqrt{x}}{\sqrt{x}+\sqrt{y}} \cdot \dfrac{\sqrt{x}-\sqrt{y}}{\sqrt{x}-\sqrt{y}} \\\\= \dfrac{x-\sqrt{xy}}{(\sqrt{x})^2-(\sqrt{y})^2} \\\\= \dfrac{x-\sqrt{xy}}{x-y} .\end{array}