Subtract $v+7$ from $ \dfrac{2}{w} $ to get $ \dfrac{ \color{purple}{ -vw-7w+2 } }{ w }$.

Step 1: Write $ v+7 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

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

$$ \begin{aligned} \frac{2}{w} -v+7 & \xlongequal{\text{Step 1}} \frac{2}{w} - \frac{v+7}{\color{red}{1}} = \frac{ 2 }{ w } - \frac{ \left( v+7 \right) \cdot \color{blue}{ w }}{ 1 \cdot \color{blue}{ w }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 2 } }{ w } - \frac{ \color{purple}{ vw+7w } }{ w }=\frac{ \color{purple}{ 2 - \left( vw+7w \right) } }{ w } = \\[1ex] &=\frac{ \color{purple}{ -vw-7w+2 } }{ w } \end{aligned} $$