Subtract $ \dfrac{1}{3} $ from $ 8x $ to get $ \dfrac{ \color{purple}{ 24x-1 } }{ 3 }$.

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

$$ \begin{aligned} 8x- \frac{1}{3} & \xlongequal{\text{Step 1}} \frac{8x}{\color{red}{1}} - \frac{1}{3} = \frac{ 8x \cdot \color{blue}{ 3 }}{ 1 \cdot \color{blue}{ 3 }} - \frac{ 1 }{ 3 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 24x } }{ 3 } - \frac{ \color{purple}{ 1 } }{ 3 }=\frac{ \color{purple}{ 24x-1 } }{ 3 } \end{aligned} $$

Add $ \dfrac{24x-1}{3} $ and $ 3x $ to get $ \dfrac{ \color{purple}{ 33x-1 } }{ 3 }$.

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

$$ \begin{aligned} \frac{24x-1}{3} +3x & \xlongequal{\text{Step 1}} \frac{24x-1}{3} + \frac{3x}{\color{red}{1}} = \frac{ 24x-1 }{ 3 } + \frac{ 3x \cdot \color{blue}{ 3 }}{ 1 \cdot \color{blue}{ 3 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 24x-1 } }{ 3 } + \frac{ \color{purple}{ 9x } }{ 3 }=\frac{ \color{purple}{ 33x-1 } }{ 3 } \end{aligned} $$

Add $ \dfrac{33x-1}{3} $ and $ \dfrac{5}{2} $ to get $ \dfrac{ \color{purple}{ 66x+13 } }{ 6 }$.

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}{ 2 }$ and the second by $\color{blue}{ 3 }$.

$$ \begin{aligned} \frac{33x-1}{3} + \frac{5}{2} & = \frac{ \left( 33x-1 \right) \cdot \color{blue}{ 2 }}{ 3 \cdot \color{blue}{ 2 }} + \frac{ 5 \cdot \color{blue}{ 3 }}{ 2 \cdot \color{blue}{ 3 }} = \\[1ex] &=\frac{ \color{purple}{ 66x-2 } }{ 6 } + \frac{ \color{purple}{ 15 } }{ 6 }=\frac{ \color{purple}{ 66x+13 } }{ 6 } \end{aligned} $$