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

$5$
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}
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