\[3\frac{7}{17} - \left( x + 1\frac{4}{17} \right) = 1\frac{9}{17}\]
\[x + 1\frac{4}{17} = 3\frac{7}{17} - 1\frac{9}{17}\]
\[x = 1\frac{15}{17} - 1\frac{4}{17}\]
\[x = \frac{11}{17}.\]