Answer
$5$
Work Step by Step
Adding the numerators and copying the denominator, 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{5x-5}{x-1}
\\\\=
\dfrac{5(x-1)}{x-1}
\\\\=
\dfrac{5(\cancel{x-1})}{\cancel{x-1}}
\\\\=
5
.\end{array}