Multiply $1$ by $ \dfrac{x^2-3x}{18} $ to get $ \dfrac{ x^2-3x }{ 18 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 1 \cdot \frac{x^2-3x}{18} & \xlongequal{\text{Step 1}} \frac{1}{\color{red}{1}} \cdot \frac{x^2-3x}{18} \xlongequal{\text{Step 2}} \frac{ 1 \cdot \left( x^2-3x \right) }{ 1 \cdot 18 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x^2-3x }{ 18 } \end{aligned} $$

Multiply $3$ by $ \dfrac{x^2-6x}{-9} $ to get $ \dfrac{ 3x^2-18x }{ -9 } $.

Step 1: Write $ 3 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 3 \cdot \frac{x^2-6x}{-9} & \xlongequal{\text{Step 1}} \frac{3}{\color{red}{1}} \cdot \frac{x^2-6x}{-9} \xlongequal{\text{Step 2}} \frac{ 3 \cdot \left( x^2-6x \right) }{ 1 \cdot \left( -9 \right) } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3x^2-18x }{ -9 } \end{aligned} $$

Multiply $1$ by $ \dfrac{x^2-3x}{18} $ to get $ \dfrac{ x^2-3x }{ 18 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 1 \cdot \frac{x^2-3x}{18} & \xlongequal{\text{Step 1}} \frac{1}{\color{red}{1}} \cdot \frac{x^2-3x}{18} \xlongequal{\text{Step 2}} \frac{ 1 \cdot \left( x^2-3x \right) }{ 1 \cdot 18 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x^2-3x }{ 18 } \end{aligned} $$

Multiply $2$ by $ \dfrac{x^2-9x+18}{18} $ to get $ \dfrac{ 2x^2-18x+36 }{ 18 } $.

Step 1: Write $ 2 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 2 \cdot \frac{x^2-9x+18}{18} & \xlongequal{\text{Step 1}} \frac{2}{\color{red}{1}} \cdot \frac{x^2-9x+18}{18} \xlongequal{\text{Step 2}} \frac{ 2 \cdot \left( x^2-9x+18 \right) }{ 1 \cdot 18 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2x^2-18x+36 }{ 18 } \end{aligned} $$

Multiply $3$ by $ \dfrac{x^2-6x}{-9} $ to get $ \dfrac{ 3x^2-18x }{ -9 } $.

Step 1: Write $ 3 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 3 \cdot \frac{x^2-6x}{-9} & \xlongequal{\text{Step 1}} \frac{3}{\color{red}{1}} \cdot \frac{x^2-6x}{-9} \xlongequal{\text{Step 2}} \frac{ 3 \cdot \left( x^2-6x \right) }{ 1 \cdot \left( -9 \right) } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3x^2-18x }{ -9 } \end{aligned} $$

Multiply $1$ by $ \dfrac{x^2-3x}{18} $ to get $ \dfrac{ x^2-3x }{ 18 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 1 \cdot \frac{x^2-3x}{18} & \xlongequal{\text{Step 1}} \frac{1}{\color{red}{1}} \cdot \frac{x^2-3x}{18} \xlongequal{\text{Step 2}} \frac{ 1 \cdot \left( x^2-3x \right) }{ 1 \cdot 18 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x^2-3x }{ 18 } \end{aligned} $$

Add $ \dfrac{2x^2-18x+36}{18} $ and $ \dfrac{3x^2-18x}{-9} $ to get $ \dfrac{ \color{purple}{ 0 } }{ 0 }$.

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}{ 0 }$ and the second by $\color{blue}{ 0 }$.

$$ \begin{aligned} \frac{2x^2-18x+36}{18} + \frac{3x^2-18x}{-9} & = \frac{ \left( 2x^2-18x+36 \right) \cdot \color{blue}{ 0 }}{ 18 \cdot \color{blue}{ 0 }} + \frac{ \left( 3x^2-18x \right) \cdot \color{blue}{ 0 }}{ \left( -9 \right) \cdot \color{blue}{ 0 }} = \\[1ex] &=\frac{ \color{purple}{ 0x^20x0 } }{ 0 } + \frac{ \color{purple}{ 0x^20x } }{ 0 }=\frac{ \color{purple}{ 0 } }{ 0 } \end{aligned} $$

Multiply $1$ by $ \dfrac{x^2-3x}{18} $ to get $ \dfrac{ x^2-3x }{ 18 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 1 \cdot \frac{x^2-3x}{18} & \xlongequal{\text{Step 1}} \frac{1}{\color{red}{1}} \cdot \frac{x^2-3x}{18} \xlongequal{\text{Step 2}} \frac{ 1 \cdot \left( x^2-3x \right) }{ 1 \cdot 18 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x^2-3x }{ 18 } \end{aligned} $$

Cannot divide by zero.

Multiply $1$ by $ \dfrac{x^2-3x}{18} $ to get $ \dfrac{ x^2-3x }{ 18 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 1 \cdot \frac{x^2-3x}{18} & \xlongequal{\text{Step 1}} \frac{1}{\color{red}{1}} \cdot \frac{x^2-3x}{18} \xlongequal{\text{Step 2}} \frac{ 1 \cdot \left( x^2-3x \right) }{ 1 \cdot 18 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x^2-3x }{ 18 } \end{aligned} $$

Add $ERROR$ and $ \dfrac{x^2-3x}{18} $ to get $ \dfrac{ \color{purple}{ x^2+18ERROR-3x } }{ 18 }$.

Step 1: Write $ ERROR $ 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 $\color{blue}{ 18 }$.

$$ \begin{aligned} ERROR+ \frac{x^2-3x}{18} & \xlongequal{\text{Step 1}} \frac{ERROR}{\color{red}{1}} + \frac{x^2-3x}{18} = \frac{ ERROR \cdot \color{blue}{ 18 }}{ 1 \cdot \color{blue}{ 18 }} + \frac{ x^2-3x }{ 18 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 18ERROR } }{ 18 } + \frac{ \color{purple}{ x^2-3x } }{ 18 }=\frac{ \color{purple}{ x^2+18ERROR-3x } }{ 18 } \end{aligned} $$