Explicação passo-a-passo:

[tex]( \frac{1}{2} - \frac{1}{3} ) \div (1 + \frac{1}{6} ) = [/tex]

[tex]( \frac{3}{6} - \frac{2}{6} ) \div ( \frac{6}{6} + \frac{1}{6} ) = [/tex]

[tex] \: \: \: \: \: \: \: ( \frac{1}{6} ) \div ( \frac{7}{6} ) = [/tex]

[tex] \: \: \: \: \: \: \: \: \: ( \frac{1}{6} ) \times ( \frac{6}{7} ) = [/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: ( \frac{1}{7}) [/tex]