Subtract $ \dfrac{v}{21} $ from $ \dfrac{v}{6} $ to get $ \dfrac{ \color{purple}{ 5v } }{ 42 }$.

To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $ \color{blue}{ 7 }$ and the second by $\color{blue}{ 2 }$.

$$ \begin{aligned} \frac{v}{6} - \frac{v}{21} & = \frac{ v \cdot \color{blue}{ 7 }}{ 6 \cdot \color{blue}{ 7 }} - \frac{ v \cdot \color{blue}{ 2 }}{ 21 \cdot \color{blue}{ 2 }} = \\[1ex] &=\frac{ \color{purple}{ 7v } }{ 42 } - \frac{ \color{purple}{ 2v } }{ 42 }=\frac{ \color{purple}{ 5v } }{ 42 } \end{aligned} $$

Subtract $ \dfrac{1}{6} $ from $ \dfrac{5v}{42} $ to get $ \dfrac{ \color{purple}{ 5v-7 } }{ 42 }$.

To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{7}$.

$$ \begin{aligned} \frac{5v}{42} - \frac{1}{6} & = \frac{ 5v }{ 42 } - \frac{ 1 \cdot \color{blue}{ 7 }}{ 6 \cdot \color{blue}{ 7 }} = \\[1ex] &=\frac{ \color{purple}{ 5v } }{ 42 } - \frac{ \color{purple}{ 7 } }{ 42 }=\frac{ \color{purple}{ 5v-7 } }{ 42 } \end{aligned} $$