#### Answer

$\dfrac{x+13}{x-1}$

#### Work Step by Step

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}