Add $ \dfrac{1}{v-5} $ and $ v $ to get $ \dfrac{ \color{purple}{ v^2-5v+1 } }{ v-5 }$.

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

Step 2: To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{v-5}$.

$$ \begin{aligned} \frac{1}{v-5} +v & \xlongequal{\text{Step 1}} \frac{1}{v-5} + \frac{v}{\color{red}{1}} = \frac{ 1 }{ v-5 } + \frac{ v \cdot \color{blue}{ \left( v-5 \right) }}{ 1 \cdot \color{blue}{ \left( v-5 \right) }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 1 } }{ v-5 } + \frac{ \color{purple}{ v^2-5v } }{ v-5 }=\frac{ \color{purple}{ v^2-5v+1 } }{ v-5 } \end{aligned} $$