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

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

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

Add $ \dfrac{x^4+9x^3+18}{x^2} $ and $ 5x $ to get $ \dfrac{ \color{purple}{ x^4+14x^3+18 } }{ x^2 }$.

Step 1: Write $ 5x $ 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 $\color{blue}{x^2}$.

$$ \begin{aligned} \frac{x^4+9x^3+18}{x^2} +5x & \xlongequal{\text{Step 1}} \frac{x^4+9x^3+18}{x^2} + \frac{5x}{\color{red}{1}} = \frac{ x^4+9x^3+18 }{ x^2 } + \frac{ 5x \cdot \color{blue}{ x^2 }}{ 1 \cdot \color{blue}{ x^2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ x^4+9x^3+18 } }{ x^2 } + \frac{ \color{purple}{ 5x^3 } }{ x^2 }=\frac{ \color{purple}{ x^4+14x^3+18 } }{ x^2 } \end{aligned} $$

Add $ \dfrac{x^4+14x^3+18}{x^2} $ and $ 6x^2 $ to get $ \dfrac{ \color{purple}{ 7x^4+14x^3+18 } }{ x^2 }$.

Step 1: Write $ 6x^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 second fraction by $\color{blue}{x^2}$.

$$ \begin{aligned} \frac{x^4+14x^3+18}{x^2} +6x^2 & \xlongequal{\text{Step 1}} \frac{x^4+14x^3+18}{x^2} + \frac{6x^2}{\color{red}{1}} = \frac{ x^4+14x^3+18 }{ x^2 } + \frac{ 6x^2 \cdot \color{blue}{ x^2 }}{ 1 \cdot \color{blue}{ x^2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ x^4+14x^3+18 } }{ x^2 } + \frac{ \color{purple}{ 6x^4 } }{ x^2 }=\frac{ \color{purple}{ 7x^4+14x^3+18 } }{ x^2 } \end{aligned} $$

Add $ \dfrac{7x^4+14x^3+18}{x^2} $ and $ 4x $ to get $ \dfrac{ \color{purple}{ 7x^4+18x^3+18 } }{ x^2 }$.

Step 1: Write $ 4x $ 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 $\color{blue}{x^2}$.

$$ \begin{aligned} \frac{7x^4+14x^3+18}{x^2} +4x & \xlongequal{\text{Step 1}} \frac{7x^4+14x^3+18}{x^2} + \frac{4x}{\color{red}{1}} = \frac{ 7x^4+14x^3+18 }{ x^2 } + \frac{ 4x \cdot \color{blue}{ x^2 }}{ 1 \cdot \color{blue}{ x^2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 7x^4+14x^3+18 } }{ x^2 } + \frac{ \color{purple}{ 4x^3 } }{ x^2 }=\frac{ \color{purple}{ 7x^4+18x^3+18 } }{ x^2 } \end{aligned} $$

Add $ \dfrac{7x^4+18x^3+18}{x^2} $ and $ \dfrac{4}{x} $ to get $ \dfrac{ \color{purple}{ 7x^5+18x^4+4x^2+18x } }{ x^3 }$.

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 }$ and the second by $\color{blue}{ x^2 }$.

$$ \begin{aligned} \frac{7x^4+18x^3+18}{x^2} + \frac{4}{x} & = \frac{ \left( 7x^4+18x^3+18 \right) \cdot \color{blue}{ x }}{ x^2 \cdot \color{blue}{ x }} + \frac{ 4 \cdot \color{blue}{ x^2 }}{ x \cdot \color{blue}{ x^2 }} = \\[1ex] &=\frac{ \color{purple}{ 7x^5+18x^4+18x } }{ x^3 } + \frac{ \color{purple}{ 4x^2 } }{ x^3 }=\frac{ \color{purple}{ 7x^5+18x^4+4x^2+18x } }{ x^3 } \end{aligned} $$