[tex]\big(\frac{1}{2} - \frac{1}{3} \bigb) - \big(\frac{1}{6}- \frac{1}{10} \big)=\big(\frac{3}{6} - \frac{2}{6} \bigb) - \big(\frac{5}{30}- \frac{3}{30} \big)=\big(\frac{3-2}{6}\bigb) - \big(\frac{5-3}{30}\big)=\frac{1}{6} - \frac{2}{30}\\\\=\frac{5}{30} - \frac{2}{30}=\frac{5-2}{30}= \frac{3^{:3}}{30_{:3}}=\frac{1}{10}[/tex]
