3 4-: 9 4

\[4 \frac{3}{9} : \frac{3}{4} = \frac{4 \cdot 9 + 3}{9} : \frac{3}{4} = \frac{39}{9} : \frac{3}{4} = \frac{39}{9} \cdot \frac{4}{3} = \frac{156}{27} = \frac{52}{9} = 5 \frac{7}{9}\]