\(\frac{4}{9}x\frac{3}{7}+\frac{5}{7}x\frac{4}{9}-\frac{4}{9}x\frac{1}{7}\)
\(=\frac{4}{9}x\left(\frac{3}{7}+\frac{5}{7}-\frac{1}{7}\right)\)
\(=\frac{4}{9}\)
\(\frac{4}{9}\times\frac{3}{7}+\frac{5}{7}\times\frac{4}{9}-\frac{4}{9}\times\frac{1}{7}\)
\(=\frac{4}{9}\times\left(\frac{3}{7}+\frac{5}{7}-\frac{1}{7}\right)\)
\(=\frac{4}{7}\times1\)
\(=\frac{4}{7}\)