[tex]\displaystyle{ 1-\frac{1}{2} :(1 - \frac{1}{2}) :[-\frac{1}{5} +(-4)\cdot (\frac{1}{3}+\frac{1}{3} : (-2) )]+\frac{1}{13} = }[/tex]
[tex]\displaystyle{ = 1 - \frac{1}{2} : \frac{2-1}{2} : [-\frac{1}{5} + (-4) \cdot (\frac{1}{3} + \frac{1}{3} \cdot \frac{-1}{2})] + \frac{1}{13} }[/tex]
[tex]\displaystyle{ = 1 - \frac{1}{2} \cdot \frac{2}{1} : [-\frac{1}{5} +(-4) \cdot (\frac{1}{3} - \frac{1}{6})]+\frac{1}{13}}[/tex]
[tex]\displaystyle{ = 1 - 1 : [-\frac{1}{5} + (-4) \cdot \frac{1}{6} ] + \frac{1}{13} }[/tex]
[tex]\displaystyle{ = 1 - 1 : (-\frac{1}{5} - \frac{4}{6}) + \frac{1}{13} }[/tex]
[tex]\displaystyle{ = 1 - 1 : (\frac{-6-20}{30}) + \frac{1}{13} }[/tex]
[tex]\displaystyle{ = 1 - 1 : \frac{-26}{30} + \frac{1}{13} }[/tex]
[tex]\displaystyle{ = 1 - 1 : \frac{-13}{10} + \frac{1}{13} }[/tex]
[tex]\displaystyle{ = 1 + \frac{10}{13} + \frac{1}{13} }[/tex]
[tex]\displaystyle{ = \frac{13+10+1}{13} }[/tex]
[tex]\displaystyle{ = \frac{24}{13} }[/tex]
