[tex]\bf 1\dfrac{3}{10} -\Big(0,(3)+\dfrac{5}{6}\Big)=[/tex]
[tex]\bf \dfrac{1\cdot10+3}{10} -\Big(\dfrac{3}{9}+\dfrac{5}{6}\Big)=[/tex]
[tex]\bf \dfrac{13}{10} -\Big(\dfrac{\not3}{\not9}+\dfrac{5}{6}\Big)=[/tex]
[tex]\bf \dfrac{13}{10} -\Big(\dfrac{1}{3}+\dfrac{5}{6}\Big)=[/tex]
[tex]\bf \dfrac{13}{10} -\Big(\dfrac{1\cdot2}{3\cdot2}+\dfrac{5}{6}\Big)=[/tex]
[tex]\bf \dfrac{13}{10} -\dfrac{2+5}{6}=[/tex]
[tex]\bf \dfrac{13}{10} -\dfrac{7}{6}=[/tex]
[tex]\bf \dfrac{13\cdot6}{10\cdot6} -\dfrac{7\cdot10}{6\cdot10}=[/tex]
[tex]\bf \dfrac{78-70}{60}=[/tex]
[tex]\bf \dfrac{8}{60}=[/tex]
[tex]\bf \dfrac{\not8}{\not60}=[/tex]
[tex]\boxed{\bf \dfrac{2}{15}}[/tex]