Add $ \dfrac{a^4b}{3} $ and $ 10a $ to get $ \dfrac{ \color{purple}{ a^4b+30a } }{ 3 }$.

Step 1: Write $ 10a $ 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 $\color{blue}{3}$.

$$ \begin{aligned} \frac{a^4b}{3} +10a & \xlongequal{\text{Step 1}} \frac{a^4b}{3} + \frac{10a}{\color{red}{1}} = \frac{ a^4b }{ 3 } + \frac{ 10a \cdot \color{blue}{ 3 }}{ 1 \cdot \color{blue}{ 3 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ a^4b } }{ 3 } + \frac{ \color{purple}{ 30a } }{ 3 }=\frac{ \color{purple}{ a^4b+30a } }{ 3 } \end{aligned} $$

Subtract $1$ from $ \dfrac{a^4b+30a}{3} $ to get $ \dfrac{ \color{purple}{ a^4b+30a-3 } }{ 3 }$.

Step 1: Write $ 1 $ 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 $\color{blue}{3}$.

$$ \begin{aligned} \frac{a^4b+30a}{3} -1 & \xlongequal{\text{Step 1}} \frac{a^4b+30a}{3} - \frac{1}{\color{red}{1}} = \frac{ a^4b+30a }{ 3 } - \frac{ 1 \cdot \color{blue}{ 3 }}{ 1 \cdot \color{blue}{ 3 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ a^4b+30a } }{ 3 } - \frac{ \color{purple}{ 3 } }{ 3 }=\frac{ \color{purple}{ a^4b+30a-3 } }{ 3 } \end{aligned} $$