Multiply $30$ by $ \dfrac{x}{x} $ to get $ \dfrac{ 30x }{ x } $.

Step 1: Write $ 30 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 30 \cdot \frac{x}{x} & \xlongequal{\text{Step 1}} \frac{30}{\color{red}{1}} \cdot \frac{x}{x} \xlongequal{\text{Step 2}} \frac{ 30 \cdot x }{ 1 \cdot x } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 30x }{ x } \end{aligned} $$

Subtract $ \dfrac{30x}{x} $ from $ 10x^2 $ to get $ \dfrac{ \color{purple}{ 10x^3-30x } }{ x }$.

Step 1: Write $ 10x^2 $ 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 $\color{blue}{ x }$.

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

Subtract $3$ from $ \dfrac{10x^3-30x}{x} $ to get $ \dfrac{ \color{purple}{ 10x^3-33x } }{ x }$.

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

$$ \begin{aligned} \frac{10x^3-30x}{x} -3 & \xlongequal{\text{Step 1}} \frac{10x^3-30x}{x} - \frac{3}{\color{red}{1}} = \frac{ 10x^3-30x }{ x } - \frac{ 3 \cdot \color{blue}{ x }}{ 1 \cdot \color{blue}{ x }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 10x^3-30x } }{ x } - \frac{ \color{purple}{ 3x } }{ x }=\frac{ \color{purple}{ 10x^3-33x } }{ x } \end{aligned} $$