Ta có: \(A=\frac{\sqrt{49}}{6}\cdot\frac{-12}{\sqrt{\left(-7\right)^4}}-\frac12\cdot\left(-\frac53\right)-\sqrt{\left(-\frac12\right)^2}\cdot\frac{\sqrt{\left(-6\right)^2}}{7}\)
\(=\frac76\cdot\frac{-12}{7^2}+\frac56-\frac12\cdot\frac67\)
\(=\frac{-2}{7}-\frac37+\frac56=-\frac57+\frac56=\frac{-30+35}{42}=\frac{5}{42}\)