Chapter 6 - Section 6.2 - Adding and Subtracting Rational Expressions - Exercise Set - Page 354: 33

$\dfrac{3}{x+4}$

Using the$LCD= (x-5)(x+4) ,$ the given expression, $ \dfrac{1}{x-5}-\dfrac{19-2x}{(x-5)(x+4)} ,$ is \begin{array}{l}\require{cancel} \dfrac{(x+4)(1)-1(19-2x)}{(x-5)(x+4)} \\\\= \dfrac{x+4-19+2x}{(x-5)(x+4)} \\\\= \dfrac{3x-15}{(x-5)(x+4)} \\\\= \dfrac{3(x-5)}{(x-5)(x+4)} \\\\= \dfrac{3(\cancel{x-5})}{(\cancel{x-5})(x+4)} \\\\= \dfrac{3}{x+4} .\end{array}