## Precalculus: Mathematics for Calculus, 7th Edition

$\dfrac{\dfrac{1}{x}-\dfrac{1}{2}}{x-2}=-\dfrac{1}{2x}$
$\dfrac{\dfrac{1}{x}-\dfrac{1}{2}}{x-2}$ Evaluate the sum of fractions in the numerator: $\dfrac{\dfrac{1}{x}-\dfrac{1}{2}}{x-2}=\dfrac{\dfrac{2-x}{2x}}{x-2}=...$ Evaluate the division: $...=\dfrac{2-x}{2x}\div(x-2)=\dfrac{2-x}{2x(x-2)}=...$ Simplify: $...=-\dfrac{x-2}{2x(x-2)}=-\dfrac{1}{2x}$