Step-by-step explanation:
[tex] \frac{1}{2} - \frac{1}{7} + \frac{1}{3} \\ \\ = \frac{1 \times 7 \times 3}{2\times 7 \times 3} - \frac{1 \times 2 \times 3}{7 \times 2 \times 3} + \frac{1 \times 2 \times 7}{3 \times 2 \times 7} \\ \\ = \frac{21}{42} - \frac{6}{42} + \frac{14}{42} \\ \\ = \frac{21 - 6 + 14}{42} \\ \\ = \frac{29}{42} \\ \\ \therefore \: \frac{1}{2} - \frac{1}{7} + \frac{1}{3} = \frac{29}{42} \\ [/tex]
