Chapter 7 - Section 7.6 - Radical Equations and Problem Solving - Exercise Set - Page 456: 90

$\dfrac{x+y}{x-y}$

The given expression, $ \dfrac{\dfrac{1}{y}+\dfrac{1}{x}}{\dfrac{1}{y}-\dfrac{1}{x}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{\dfrac{x(1)+y(1)}{xy}}{\dfrac{x(1)-y(1)}{xy}} \\\\= \dfrac{\dfrac{x(1)+y(1)}{\cancel{xy}}}{\dfrac{x(1)-y(1)}{\cancel{xy}}} \\\\= \dfrac{x(1)+y(1)}{x(1)-y(1)} \\\\= \dfrac{x+y}{x-y} .\end{array}