Multiply $b$ by $ \dfrac{c^5}{3} $ to get $ \dfrac{ bc^5 }{ 3 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} b \cdot \frac{c^5}{3} & \xlongequal{\text{Step 1}} \frac{b}{\color{red}{1}} \cdot \frac{c^5}{3} \xlongequal{\text{Step 2}} \frac{ b \cdot c^5 }{ 1 \cdot 3 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ bc^5 }{ 3 } \end{aligned} $$

Add $8c+3$ and $ \dfrac{bc^5}{3} $ to get $ \dfrac{ \color{purple}{ bc^5+24c+9 } }{ 3 }$.

Step 1: Write $ 8c+3 $ 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 first fraction by $\color{blue}{ 3 }$.

$$ \begin{aligned} 8c+3+ \frac{bc^5}{3} & \xlongequal{\text{Step 1}} \frac{8c+3}{\color{red}{1}} + \frac{bc^5}{3} = \frac{ \left( 8c+3 \right) \cdot \color{blue}{ 3 }}{ 1 \cdot \color{blue}{ 3 }} + \frac{ bc^5 }{ 3 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 24c+9 } }{ 3 } + \frac{ \color{purple}{ bc^5 } }{ 3 }=\frac{ \color{purple}{ bc^5+24c+9 } }{ 3 } \end{aligned} $$