$\frac{-3}{5}<x<\frac{1}{7}$
$→\left\{{{\frac{-3}{5}<x}\atop{x<\frac{1}{7}}}\right.$
$→\left\{{{-x-\frac{3}{5}<0}\atop{-x+\frac{1}{7}>0}}\right.$
$A=\Big|-x+\frac{1}{7}\Big|+\Big|-x-\frac{3}{5}\Big|-\frac{2}{6}$
$=-x+\frac{1}{7}+x+\frac{3}{5}-\frac{2}{6}=\frac{43}{105}$