## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$\dfrac{x+13}{x-1}$
When subtracting two fractions with common denominators, we subtract the numerators and copy the denominator. Therefore, the given expression, $\dfrac{3x+4}{x-1}-\dfrac{2x-9}{x-1} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{3x+4-(2x-9)}{x-1} \\\\= \dfrac{3x+4-2x+9}{x-1} \\\\= \dfrac{x+13}{x-1} .\end{array}