[tex]\displaystyle\bf\\\frac{a}{b}=\frac{3}{4}\\\\\\\frac{2a+3b}{4b}=\\\\\\=\frac{2a}{4b}+\frac{3b}{4b}=\\\\\\=\frac{2}{4}\times\frac{a}{b}+\frac{3}{4}=\\\\\\=\frac{2}{4}\times\frac{3}{7}+\frac{3}{4}=\\\\\\=\frac{2\times3}{4\times7}+\frac{3}{4}=\\\\\\=\frac{6}{28}+\frac{^{7)}3}{~~4}=\\\\\\=\frac{6}{28}+\frac{21}{28}=\\\\\\=\frac{6+21}{28}=\\\\\\=\boxed{\bf\frac{27}{28}}[/tex]
