Combine like terms:

$$ \color{blue}{2x} + \color{blue}{8x} = \color{blue}{10x} $$

Add $10x$ and $ \dfrac{15}{x^2} $ to get $ \dfrac{ \color{purple}{ 10x^3+15 } }{ x^2 }$.

Step 1: Write $ 10x $ 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 $\color{blue}{ x^2 }$.

$$ \begin{aligned} 10x+ \frac{15}{x^2} & \xlongequal{\text{Step 1}} \frac{10x}{\color{red}{1}} + \frac{15}{x^2} = \frac{ 10x \cdot \color{blue}{ x^2 }}{ 1 \cdot \color{blue}{ x^2 }} + \frac{ 15 }{ x^2 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 10x^3 } }{ x^2 } + \frac{ \color{purple}{ 15 } }{ x^2 }=\frac{ \color{purple}{ 10x^3+15 } }{ x^2 } \end{aligned} $$

Subtract $x$ from $ \dfrac{10x^3+15}{x^2} $ to get $ \dfrac{ \color{purple}{ 9x^3+15 } }{ x^2 }$.

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

$$ \begin{aligned} \frac{10x^3+15}{x^2} -x & \xlongequal{\text{Step 1}} \frac{10x^3+15}{x^2} - \frac{x}{\color{red}{1}} = \frac{ 10x^3+15 }{ x^2 } - \frac{ x \cdot \color{blue}{ x^2 }}{ 1 \cdot \color{blue}{ x^2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 10x^3+15 } }{ x^2 } - \frac{ \color{purple}{ x^3 } }{ x^2 }=\frac{ \color{purple}{ 9x^3+15 } }{ x^2 } \end{aligned} $$

Subtract $12$ from $ \dfrac{9x^3+15}{x^2} $ to get $ \dfrac{ \color{purple}{ 9x^3-12x^2+15 } }{ x^2 }$.

Step 1: Write $ 12 $ 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 $\color{blue}{x^2}$.

$$ \begin{aligned} \frac{9x^3+15}{x^2} -12 & \xlongequal{\text{Step 1}} \frac{9x^3+15}{x^2} - \frac{12}{\color{red}{1}} = \frac{ 9x^3+15 }{ x^2 } - \frac{ 12 \cdot \color{blue}{ x^2 }}{ 1 \cdot \color{blue}{ x^2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 9x^3+15 } }{ x^2 } - \frac{ \color{purple}{ 12x^2 } }{ x^2 }=\frac{ \color{purple}{ 9x^3-12x^2+15 } }{ x^2 } \end{aligned} $$