Multiply $16$ by $ \dfrac{x}{x^2} $ to get $ \dfrac{ 16x }{ x^2 } $.

Step 1: Write $ 16 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 16 \cdot \frac{x}{x^2} & \xlongequal{\text{Step 1}} \frac{16}{\color{red}{1}} \cdot \frac{x}{x^2} \xlongequal{\text{Step 2}} \frac{ 16 \cdot x }{ 1 \cdot x^2 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 16x }{ x^2 } \end{aligned} $$

Add $2x^2$ and $ \dfrac{16x}{x^2} $ to get $ \dfrac{ \color{purple}{ 2x^4+16x } }{ x^2 }$.

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

$$ \begin{aligned} 2x^2+ \frac{16x}{x^2} & \xlongequal{\text{Step 1}} \frac{2x^2}{\color{red}{1}} + \frac{16x}{x^2} = \frac{ 2x^2 \cdot \color{blue}{ x^2 }}{ 1 \cdot \color{blue}{ x^2 }} + \frac{ 16x }{ x^2 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 2x^4 } }{ x^2 } + \frac{ \color{purple}{ 16x } }{ x^2 }=\frac{ \color{purple}{ 2x^4+16x } }{ x^2 } \end{aligned} $$

Subtract $9x$ from $ \dfrac{2x^4+16x}{x^2} $ to get $ \dfrac{ \color{purple}{ 2x^4-9x^3+16x } }{ x^2 }$.

Step 1: Write $ 9x $ 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 $\color{blue}{x^2}$.

$$ \begin{aligned} \frac{2x^4+16x}{x^2} -9x & \xlongequal{\text{Step 1}} \frac{2x^4+16x}{x^2} - \frac{9x}{\color{red}{1}} = \frac{ 2x^4+16x }{ x^2 } - \frac{ 9x \cdot \color{blue}{ x^2 }}{ 1 \cdot \color{blue}{ x^2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 2x^4+16x } }{ x^2 } - \frac{ \color{purple}{ 9x^3 } }{ x^2 }=\frac{ \color{purple}{ 2x^4-9x^3+16x } }{ x^2 } \end{aligned} $$

Add $ \dfrac{2x^4-9x^3+16x}{x^2} $ and $ 18 $ to get $ \dfrac{ \color{purple}{ 2x^4-9x^3+18x^2+16x } }{ x^2 }$.

Step 1: Write $ 18 $ 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 $\color{blue}{x^2}$.

$$ \begin{aligned} \frac{2x^4-9x^3+16x}{x^2} +18 & \xlongequal{\text{Step 1}} \frac{2x^4-9x^3+16x}{x^2} + \frac{18}{\color{red}{1}} = \frac{ 2x^4-9x^3+16x }{ x^2 } + \frac{ 18 \cdot \color{blue}{ x^2 }}{ 1 \cdot \color{blue}{ x^2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 2x^4-9x^3+16x } }{ x^2 } + \frac{ \color{purple}{ 18x^2 } }{ x^2 }=\frac{ \color{purple}{ 2x^4-9x^3+18x^2+16x } }{ x^2 } \end{aligned} $$