Subtract $ \dfrac{63}{x} $ from $ x^2+2x $ to get $ \dfrac{ \color{purple}{ x^3+2x^2-63 } }{ x }$.

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

$$ \begin{aligned} x^2+2x- \frac{63}{x} & \xlongequal{\text{Step 1}} \frac{x^2+2x}{\color{red}{1}} - \frac{63}{x} = \frac{ \left( x^2+2x \right) \cdot \color{blue}{ x }}{ 1 \cdot \color{blue}{ x }} - \frac{ 63 }{ x } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ x^3+2x^2 } }{ x } - \frac{ \color{purple}{ 63 } }{ x }=\frac{ \color{purple}{ x^3+2x^2-63 } }{ x } \end{aligned} $$

Add $ \dfrac{x^3+2x^2-63}{x} $ and $ 9 $ to get $ \dfrac{ \color{purple}{ x^3+2x^2+9x-63 } }{ x }$.

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

$$ \begin{aligned} \frac{x^3+2x^2-63}{x} +9 & \xlongequal{\text{Step 1}} \frac{x^3+2x^2-63}{x} + \frac{9}{\color{red}{1}} = \frac{ x^3+2x^2-63 }{ x } + \frac{ 9 \cdot \color{blue}{ x }}{ 1 \cdot \color{blue}{ x }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ x^3+2x^2-63 } }{ x } + \frac{ \color{purple}{ 9x } }{ x }=\frac{ \color{purple}{ x^3+2x^2+9x-63 } }{ x } \end{aligned} $$