$$ 2 x^2 x^4 = 2 x^{2 + 4} = 2 x^6 $$

Divide both the top and bottom numbers by $ \color{orangered}{ 18 } $.

Multiply $3$ by $ \dfrac{x^2}{x^2} $ to get $ \dfrac{ 3x^2 }{ x^2 } $.

Step 1: Write $ 3 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Multiply $3$ by $ \dfrac{x^2}{x^2} $ to get $ \dfrac{ 3x^2 }{ x^2 } $.

Step 1: Write $ 3 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Remove 1 from denominator.

Multiply $3$ by $ \dfrac{x^2}{x^2} $ to get $ \dfrac{ 3x^2 }{ x^2 } $.

Step 1: Write $ 3 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Combine like terms:

$$ x^2+ \color{blue}{5x} \color{blue}{-2x} = x^2+ \color{blue}{3x} $$

Multiply $3$ by $ \dfrac{x^2}{x^2} $ to get $ \dfrac{ 3x^2 }{ x^2 } $.

Step 1: Write $ 3 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Add $x^2+3x-2x^6+4x^3$ and $ \dfrac{3x^2}{x^2} $ to get $ \dfrac{ \color{purple}{ -2x^8+4x^5+x^4+3x^3+3x^2 } }{ x^2 }$.

Step 1: Write $ x^2+3x-2x^6+4x^3 $ 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 $\color{blue}{ x^2 }$.

$$ \begin{aligned} x^2+3x-2x^6+4x^3+ \frac{3x^2}{x^2} & \xlongequal{\text{Step 1}} \frac{x^2+3x-2x^6+4x^3}{\color{red}{1}} + \frac{3x^2}{x^2} = \frac{ \left( x^2+3x-2x^6+4x^3 \right) \cdot \color{blue}{ x^2 }}{ 1 \cdot \color{blue}{ x^2 }} + \frac{ 3x^2 }{ x^2 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ x^4+3x^3-2x^8+4x^5 } }{ x^2 } + \frac{ \color{purple}{ 3x^2 } }{ x^2 }=\frac{ \color{purple}{ -2x^8+4x^5+x^4+3x^3+3x^2 } }{ x^2 } \end{aligned} $$

Add $ \dfrac{-2x^8+4x^5+x^4+3x^3+3x^2}{x^2} $ and $ 10x $ to get $ \dfrac{ \color{purple}{ -2x^8+4x^5+x^4+13x^3+3x^2 } }{ 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 second fraction by $\color{blue}{x^2}$.

$$ \begin{aligned} \frac{-2x^8+4x^5+x^4+3x^3+3x^2}{x^2} +10x & \xlongequal{\text{Step 1}} \frac{-2x^8+4x^5+x^4+3x^3+3x^2}{x^2} + \frac{10x}{\color{red}{1}} = \\[1ex] &= \frac{ -2x^8+4x^5+x^4+3x^3+3x^2 }{ x^2 } + \frac{ 10x \cdot \color{blue}{ x^2 }}{ 1 \cdot \color{blue}{ x^2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -2x^8+4x^5+x^4+3x^3+3x^2 } }{ x^2 } + \frac{ \color{purple}{ 10x^3 } }{ x^2 }=\frac{ \color{purple}{ -2x^8+4x^5+x^4+13x^3+3x^2 } }{ x^2 } \end{aligned} $$

Add $ \dfrac{-2x^8+4x^5+x^4+13x^3+3x^2}{x^2} $ and $ 9 $ to get $ \dfrac{ \color{purple}{ -2x^8+4x^5+x^4+13x^3+12x^2 } }{ x^2 }$.

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 $\color{blue}{x^2}$.

$$ \begin{aligned} \frac{-2x^8+4x^5+x^4+13x^3+3x^2}{x^2} +9 & \xlongequal{\text{Step 1}} \frac{-2x^8+4x^5+x^4+13x^3+3x^2}{x^2} + \frac{9}{\color{red}{1}} = \\[1ex] &= \frac{ -2x^8+4x^5+x^4+13x^3+3x^2 }{ x^2 } + \frac{ 9 \cdot \color{blue}{ x^2 }}{ 1 \cdot \color{blue}{ x^2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -2x^8+4x^5+x^4+13x^3+3x^2 } }{ x^2 } + \frac{ \color{purple}{ 9x^2 } }{ x^2 }=\frac{ \color{purple}{ -2x^8+4x^5+x^4+13x^3+12x^2 } }{ x^2 } \end{aligned} $$