College Algebra (6th Edition)

$(3x + 4)$
To find equivalent expressions of fractions, we can only multiply by $1$, and any fraction that solves into $1$. Therefore, to find an equivalent expression for $\frac{3x + 2}{x - 5}$ with a denominator $(3x + 4)(x - 5)$, we multiply by $1$: $$\frac{3x + 2}{x - 5} \times 1 = \frac{3x + 2}{x - 5} \times \frac{3x + 4}{3x + 4}$$ $= \frac{(3x + 2)(3x + 4)}{(x - 5)(3x + 4)}$ which satisfies the conditions of the exercise.