Multiply $ \dfrac{9}{k} $ by $ 2 $ to get $ \dfrac{ 18 }{ k } $.

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.

$$ \begin{aligned} \frac{9}{k} \cdot 2 & \xlongequal{\text{Step 1}} \frac{9}{k} \cdot \frac{2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 9 \cdot 2 }{ k \cdot 1 } \xlongequal{\text{Step 3}} \frac{ 18 }{ k } \end{aligned} $$

Subtract $ \dfrac{18}{k} $ from $ k $ to get $ \dfrac{ \color{purple}{ k^2-18 } }{ k }$.

Step 1: Write $ k $ 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 $\color{blue}{ k }$.

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

Subtract $12k$ from $ \dfrac{k^2-18}{k} $ to get $ \dfrac{ \color{purple}{ -11k^2-18 } }{ k }$.

Step 1: Write $ 12k $ 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 $\color{blue}{k}$.

$$ \begin{aligned} \frac{k^2-18}{k} -12k & \xlongequal{\text{Step 1}} \frac{k^2-18}{k} - \frac{12k}{\color{red}{1}} = \frac{ k^2-18 }{ k } - \frac{ 12k \cdot \color{blue}{ k }}{ 1 \cdot \color{blue}{ k }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ k^2-18 } }{ k } - \frac{ \color{purple}{ 12k^2 } }{ k }=\frac{ \color{purple}{ -11k^2-18 } }{ k } \end{aligned} $$

Add $ \dfrac{-11k^2-18}{k} $ and $ 27 $ to get $ \dfrac{ \color{purple}{ -11k^2+27k-18 } }{ k }$.

Step 1: Write $ 27 $ 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 $\color{blue}{k}$.

$$ \begin{aligned} \frac{-11k^2-18}{k} +27 & \xlongequal{\text{Step 1}} \frac{-11k^2-18}{k} + \frac{27}{\color{red}{1}} = \frac{ -11k^2-18 }{ k } + \frac{ 27 \cdot \color{blue}{ k }}{ 1 \cdot \color{blue}{ k }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -11k^2-18 } }{ k } + \frac{ \color{purple}{ 27k } }{ k }=\frac{ \color{purple}{ -11k^2+27k-18 } }{ k } \end{aligned} $$