Divide the sum of $\dfrac{3}{7}$ and $\dfrac{-5}{14}$ by $-\dfrac{1}{2}$.

The sum of $\dfrac{3}{7}$ and $\dfrac{-5}{14}$

$\dfrac{3}{7} + \dfrac{-5}{14}$

LCM of 7 and 14 is 2 x 7 = 14

$= \dfrac{3 \times 2}{7 \times 2} + \dfrac{-5 \times 1}{14 \times 1}\\[1em] = \dfrac{6}{14} + \dfrac{-5}{14}\\[1em] = \dfrac{6 + (-5)}{14}\\[1em] = \dfrac{1}{14}$

Dividing the sum of $\dfrac{3}{7}$ and $\dfrac{-5}{14}$ by $-\dfrac{1}{2}$

$\dfrac{1}{14} ÷ -\dfrac{1}{2}\\[1em] = \dfrac{1}{14} \times -\dfrac{2}{1}\\[1em] = -\dfrac{1 \times 2}{14 \times 1}\\[1em] = -\dfrac{2}{14}\\[1em] = -\dfrac{1}{7}$

On dividing the sum of $\dfrac{3}{7}$ and $\dfrac{-5}{14}$ by $-\dfrac{1}{2}$ we get $-\dfrac{1}{7}$.