\(\frac{1}{5}\cdot\frac{1}{7}+\frac{4}{5}+\frac{1}{5}\cdot\frac{12}{7}-1-\frac{1}{5}\cdot\frac{6}{7}\)
\(=\frac{1}{5}\cdot\left(\frac{1}{7}+\frac{12}{7}-\frac{6}{7}\right)-\left(1-\frac{4}{5}\right)\)
\(=\frac{1}{5}.1-\frac{1}{5}\)
\(=\frac{1}{5}-\frac{1}{5}=0\)