Multiply $9$ by $ \dfrac{x}{3} $ to get $ \dfrac{ 9x }{ 3 } $.

Step 1: Write $ 9 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 9 \cdot \frac{x}{3} & \xlongequal{\text{Step 1}} \frac{9}{\color{red}{1}} \cdot \frac{x}{3} \xlongequal{\text{Step 2}} \frac{ 9 \cdot x }{ 1 \cdot 3 } \xlongequal{\text{Step 3}} \frac{ 9x }{ 3 } \end{aligned} $$

Multiply $ \dfrac{9x}{3} $ by $ x $ to get $ \dfrac{ 9x^2 }{ 3 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{9x}{3} \cdot x & \xlongequal{\text{Step 1}} \frac{9x}{3} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 9x \cdot x }{ 3 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 9x^2 }{ 3 } \end{aligned} $$

Subtract $ \dfrac{9x^2}{3} $ from $ x^2 $ to get $ \dfrac{ \color{purple}{ -6x^2 } }{ 3 }$.

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

$$ \begin{aligned} x^2- \frac{9x^2}{3} & \xlongequal{\text{Step 1}} \frac{x^2}{\color{red}{1}} - \frac{9x^2}{3} = \frac{ x^2 \cdot \color{blue}{ 3 }}{ 1 \cdot \color{blue}{ 3 }} - \frac{ 9x^2 }{ 3 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 3x^2 } }{ 3 } - \frac{ \color{purple}{ 9x^2 } }{ 3 }=\frac{ \color{purple}{ -6x^2 } }{ 3 } \end{aligned} $$