Multiply $ \dfrac{7t^3-31t-20}{7} $ by $ t $ to get $ \dfrac{ 7t^4-31t^2-20t }{ 7 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{7t^3-31t-20}{7} \cdot t & \xlongequal{\text{Step 1}} \frac{7t^3-31t-20}{7} \cdot \frac{t}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( 7t^3-31t-20 \right) \cdot t }{ 7 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 7t^4-31t^2-20t }{ 7 } \end{aligned} $$

Add $ \dfrac{7t^4-31t^2-20t}{7} $ and $ 4 $ to get $ \dfrac{ \color{purple}{ 7t^4-31t^2-20t+28 } }{ 7 }$.

Step 1: Write $ 4 $ 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 $\color{blue}{7}$.

$$ \begin{aligned} \frac{7t^4-31t^2-20t}{7} +4 & \xlongequal{\text{Step 1}} \frac{7t^4-31t^2-20t}{7} + \frac{4}{\color{red}{1}} = \frac{ 7t^4-31t^2-20t }{ 7 } + \frac{ 4 \cdot \color{blue}{ 7 }}{ 1 \cdot \color{blue}{ 7 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 7t^4-31t^2-20t } }{ 7 } + \frac{ \color{purple}{ 28 } }{ 7 }=\frac{ \color{purple}{ 7t^4-31t^2-20t+28 } }{ 7 } \end{aligned} $$