$\boldsymbol{\frac{x - 3}{6} - \frac{x - 1}{10} = \frac{1}{6}(x - 3) - \frac{1}{10}(x - 1)}$
$\boldsymbol{= \frac{1}{6}x - \frac{1}{2} - \frac{1}{10}x + \frac{1}{10}}$
$\boldsymbol{= \left( \frac{1}{6} - \frac{1}{10} \right)x - \frac{1}{2} + \frac{1}{10}}$
$\boldsymbol{= \left( \frac{5 - 3}{30} \right)x - \frac{5 - 1}{10} = \frac{1}{15}x - \frac{2}{5}}$.