\(\begin{array}{l}\frac{{3a - b}}{{a + b}} = \frac{3}{4}\\ \Rightarrow 4\left( {3a - b} \right) = 3\left( {a + b} \right)\\ \Rightarrow 12a - 4b = 3a + 3b\\ \Rightarrow 12a - 3a = 3b + 4b\\ \Leftrightarrow \,\,\,9a = 7b\\ \Rightarrow \frac{a}{b} = \frac{7}{9}\end{array}\)