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

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

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

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

Step 1: Write $ 3x $ 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 $\color{blue}{x^2}$.

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

Subtract $ \dfrac{10}{x^2} $ from $ \dfrac{x^4+3x^3-4}{x^2} $ to get $ \dfrac{x^4+3x^3-14}{x^2} $.

To subtract expressions with the same denominators, we subtract the numerators and write the result over the common denominator.

$$ \begin{aligned} \frac{x^4+3x^3-4}{x^2} - \frac{10}{x^2} & = \frac{x^4+3x^3-4}{\color{blue}{x^2}} - \frac{10}{\color{blue}{x^2}} = \\[1ex] &=\frac{ x^4+3x^3-4 - 10 }{ \color{blue}{ x^2 }}= \frac{x^4+3x^3-14}{x^2} \end{aligned} $$

Add $ \dfrac{x^4+3x^3-14}{x^2} $ and $ 5x $ to get $ \dfrac{ \color{purple}{ x^4+8x^3-14 } }{ 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 $\color{blue}{x^2}$.

$$ \begin{aligned} \frac{x^4+3x^3-14}{x^2} +5x & \xlongequal{\text{Step 1}} \frac{x^4+3x^3-14}{x^2} + \frac{5x}{\color{red}{1}} = \frac{ x^4+3x^3-14 }{ x^2 } + \frac{ 5x \cdot \color{blue}{ x^2 }}{ 1 \cdot \color{blue}{ x^2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ x^4+3x^3-14 } }{ x^2 } + \frac{ \color{purple}{ 5x^3 } }{ x^2 }=\frac{ \color{purple}{ x^4+8x^3-14 } }{ x^2 } \end{aligned} $$

Add $ \dfrac{x^4+8x^3-14}{x^2} $ and $ \dfrac{6}{x^2} $ to get $ \dfrac{x^4+8x^3-8}{x^2} $.

To add expressions with the same denominators, we add the numerators and write the result over the common denominator.

$$ \begin{aligned} \frac{x^4+8x^3-14}{x^2} + \frac{6}{x^2} & = \frac{x^4+8x^3-14}{\color{blue}{x^2}} + \frac{6}{\color{blue}{x^2}} = \\[1ex] &=\frac{ x^4+8x^3-14 + 6 }{ \color{blue}{ x^2 }}= \frac{x^4+8x^3-8}{x^2} \end{aligned} $$

Add $ \dfrac{x^4+8x^3-8}{x^2} $ and $ 8x $ to get $ \dfrac{ \color{purple}{ x^4+16x^3-8 } }{ x^2 }$.

Step 1: Write $ 8x $ 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 $\color{blue}{x^2}$.

$$ \begin{aligned} \frac{x^4+8x^3-8}{x^2} +8x & \xlongequal{\text{Step 1}} \frac{x^4+8x^3-8}{x^2} + \frac{8x}{\color{red}{1}} = \frac{ x^4+8x^3-8 }{ x^2 } + \frac{ 8x \cdot \color{blue}{ x^2 }}{ 1 \cdot \color{blue}{ x^2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ x^4+8x^3-8 } }{ x^2 } + \frac{ \color{purple}{ 8x^3 } }{ x^2 }=\frac{ \color{purple}{ x^4+16x^3-8 } }{ x^2 } \end{aligned} $$

Add $ \dfrac{x^4+16x^3-8}{x^2} $ and $ 15 $ to get $ \dfrac{ \color{purple}{ x^4+16x^3+15x^2-8 } }{ x^2 }$.

Step 1: Write $ 15 $ 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 $\color{blue}{x^2}$.

$$ \begin{aligned} \frac{x^4+16x^3-8}{x^2} +15 & \xlongequal{\text{Step 1}} \frac{x^4+16x^3-8}{x^2} + \frac{15}{\color{red}{1}} = \frac{ x^4+16x^3-8 }{ x^2 } + \frac{ 15 \cdot \color{blue}{ x^2 }}{ 1 \cdot \color{blue}{ x^2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ x^4+16x^3-8 } }{ x^2 } + \frac{ \color{purple}{ 15x^2 } }{ x^2 }=\frac{ \color{purple}{ x^4+16x^3+15x^2-8 } }{ x^2 } \end{aligned} $$