Chapter 6 - Section 6.2 - Adding and Subtracting Rational Expressions - Exercise Set - Page 354: 34

$\dfrac{2}{x-5}$

Using the$LCD= (x-5)(x+4) ,$ the given expression, $ \dfrac{4x-2}{(x-5)(x+4)}-\dfrac{2}{x+4} ,$ is \begin{array}{l}\require{cancel} \dfrac{1(4x-2)-(x-5)(2)}{(x-5)(x+4)} \\\\= \dfrac{4x-2-2x+10}{(x-5)(x+4)} \\\\= \dfrac{2x+8}{(x-5)(x+4)} \\\\= \dfrac{2(x+4)}{(x-5)(x+4)} \\\\= \dfrac{2(\cancel{x+4})}{(x-5)(\cancel{x+4})} \\\\= \dfrac{2}{x-5} .\end{array}