Multiply $ \dfrac{n+6}{10} $ by $ n $ to get $ \dfrac{ n^2+6n }{ 10 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{n+6}{10} \cdot n & \xlongequal{\text{Step 1}} \frac{n+6}{10} \cdot \frac{n}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( n+6 \right) \cdot n }{ 10 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ n^2+6n }{ 10 } \end{aligned} $$

Add $ \dfrac{n^2+6n}{10} $ and $ 60 $ to get $ \dfrac{ \color{purple}{ n^2+6n+600 } }{ 10 }$.

Step 1: Write $ 60 $ 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 $\color{blue}{10}$.

$$ \begin{aligned} \frac{n^2+6n}{10} +60 & \xlongequal{\text{Step 1}} \frac{n^2+6n}{10} + \frac{60}{\color{red}{1}} = \frac{ n^2+6n }{ 10 } + \frac{ 60 \cdot \color{blue}{ 10 }}{ 1 \cdot \color{blue}{ 10 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ n^2+6n } }{ 10 } + \frac{ \color{purple}{ 600 } }{ 10 }=\frac{ \color{purple}{ n^2+6n+600 } }{ 10 } \end{aligned} $$