Add $13$ and $ \dfrac{x^2}{15} $ to get $ \dfrac{ \color{purple}{ x^2+195 } }{ 15 }$.

Step 1: Write $ 13 $ 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 $\color{blue}{ 15 }$.

$$ \begin{aligned} 13+ \frac{x^2}{15} & \xlongequal{\text{Step 1}} \frac{13}{\color{red}{1}} + \frac{x^2}{15} = \frac{ 13 \cdot \color{blue}{ 15 }}{ 1 \cdot \color{blue}{ 15 }} + \frac{ x^2 }{ 15 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 195 } }{ 15 } + \frac{ \color{purple}{ x^2 } }{ 15 }=\frac{ \color{purple}{ x^2+195 } }{ 15 } \end{aligned} $$

Divide $x^2$ by $ \dfrac{x^2+195}{15} $ to get $ \dfrac{ 15x^2 }{ x^2+195 } $.

Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction.

Step 2: Write $ x^2 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 3: Multiply numerators and denominators.

Step 4: Simplify numerator and denominator.

$$ \begin{aligned} \frac{x^2}{ \frac{\color{blue}{x^2+195}}{\color{blue}{15}} } & \xlongequal{\text{Step 1}} x^2 \cdot \frac{\color{blue}{15}}{\color{blue}{x^2+195}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{x^2}{\color{red}{1}} \cdot \frac{15}{x^2+195} \xlongequal{\text{Step 3}} \frac{ x^2 \cdot 15 }{ 1 \cdot \left( x^2+195 \right) } = \\[1ex] & \xlongequal{\text{Step 4}} \frac{ 15x^2 }{ x^2+195 } \end{aligned} $$

Add $11$ and $ \dfrac{15x^2}{x^2+195} $ to get $ \dfrac{ \color{purple}{ 26x^2+2145 } }{ x^2+195 }$.

Step 1: Write $ 11 $ 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 $\color{blue}{ x^2+195 }$.

$$ \begin{aligned} 11+ \frac{15x^2}{x^2+195} & \xlongequal{\text{Step 1}} \frac{11}{\color{red}{1}} + \frac{15x^2}{x^2+195} = \frac{ 11 \cdot \color{blue}{ \left( x^2+195 \right) }}{ 1 \cdot \color{blue}{ \left( x^2+195 \right) }} + \frac{ 15x^2 }{ x^2+195 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 11x^2+2145 } }{ x^2+195 } + \frac{ \color{purple}{ 15x^2 } }{ x^2+195 }=\frac{ \color{purple}{ 26x^2+2145 } }{ x^2+195 } \end{aligned} $$

Divide $x^2$ by $ \dfrac{26x^2+2145}{x^2+195} $ to get $ \dfrac{ x^4+195x^2 }{ 26x^2+2145 } $.

Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction.

Step 2: Write $ x^2 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 3: Multiply numerators and denominators.

Step 4: Simplify numerator and denominator.

$$ \begin{aligned} \frac{x^2}{ \frac{\color{blue}{26x^2+2145}}{\color{blue}{x^2+195}} } & \xlongequal{\text{Step 1}} x^2 \cdot \frac{\color{blue}{x^2+195}}{\color{blue}{26x^2+2145}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{x^2}{\color{red}{1}} \cdot \frac{x^2+195}{26x^2+2145} \xlongequal{\text{Step 3}} \frac{ x^2 \cdot \left( x^2+195 \right) }{ 1 \cdot \left( 26x^2+2145 \right) } = \\[1ex] & \xlongequal{\text{Step 4}} \frac{ x^4+195x^2 }{ 26x^2+2145 } \end{aligned} $$

Add $9$ and $ \dfrac{x^4+195x^2}{26x^2+2145} $ to get $ \dfrac{ \color{purple}{ x^4+429x^2+19305 } }{ 26x^2+2145 }$.

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 first fraction by $\color{blue}{ 26x^2+2145 }$.

$$ \begin{aligned} 9+ \frac{x^4+195x^2}{26x^2+2145} & \xlongequal{\text{Step 1}} \frac{9}{\color{red}{1}} + \frac{x^4+195x^2}{26x^2+2145} = \frac{ 9 \cdot \color{blue}{ \left( 26x^2+2145 \right) }}{ 1 \cdot \color{blue}{ \left( 26x^2+2145 \right) }} + \frac{ x^4+195x^2 }{ 26x^2+2145 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 234x^2+19305 } }{ 26x^2+2145 } + \frac{ \color{purple}{ x^4+195x^2 } }{ 26x^2+2145 } = \\[1ex] &=\frac{ \color{purple}{ x^4+429x^2+19305 } }{ 26x^2+2145 } \end{aligned} $$

Divide $x^2$ by $ \dfrac{x^4+429x^2+19305}{26x^2+2145} $ to get $ \dfrac{ 26x^4+2145x^2 }{ x^4+429x^2+19305 } $.

Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction.

Step 2: Write $ x^2 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 3: Multiply numerators and denominators.

Step 4: Simplify numerator and denominator.

$$ \begin{aligned} \frac{x^2}{ \frac{\color{blue}{x^4+429x^2+19305}}{\color{blue}{26x^2+2145}} } & \xlongequal{\text{Step 1}} x^2 \cdot \frac{\color{blue}{26x^2+2145}}{\color{blue}{x^4+429x^2+19305}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{x^2}{\color{red}{1}} \cdot \frac{26x^2+2145}{x^4+429x^2+19305} \xlongequal{\text{Step 3}} \frac{ x^2 \cdot \left( 26x^2+2145 \right) }{ 1 \cdot \left( x^4+429x^2+19305 \right) } = \\[1ex] & \xlongequal{\text{Step 4}} \frac{ 26x^4+2145x^2 }{ x^4+429x^2+19305 } \end{aligned} $$

Add $7$ and $ \dfrac{26x^4+2145x^2}{x^4+429x^2+19305} $ to get $ \dfrac{ \color{purple}{ 33x^4+5148x^2+135135 } }{ x^4+429x^2+19305 }$.

Step 1: Write $ 7 $ 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 $\color{blue}{ x^4+429x^2+19305 }$.

$$ \begin{aligned} 7+ \frac{26x^4+2145x^2}{x^4+429x^2+19305} & \xlongequal{\text{Step 1}} \frac{7}{\color{red}{1}} + \frac{26x^4+2145x^2}{x^4+429x^2+19305} = \\[1ex] &= \frac{ 7 \cdot \color{blue}{ \left( x^4+429x^2+19305 \right) }}{ 1 \cdot \color{blue}{ \left( x^4+429x^2+19305 \right) }} + \frac{ 26x^4+2145x^2 }{ x^4+429x^2+19305 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 7x^4+3003x^2+135135 } }{ x^4+429x^2+19305 } + \frac{ \color{purple}{ 26x^4+2145x^2 } }{ x^4+429x^2+19305 } = \\[1ex] &=\frac{ \color{purple}{ 33x^4+5148x^2+135135 } }{ x^4+429x^2+19305 } \end{aligned} $$

Divide $x^2$ by $ \dfrac{33x^4+5148x^2+135135}{x^4+429x^2+19305} $ to get $ \dfrac{ x^6+429x^4+19305x^2 }{ 33x^4+5148x^2+135135 } $.

Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction.

Step 2: Write $ x^2 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 3: Multiply numerators and denominators.

Step 4: Simplify numerator and denominator.

$$ \begin{aligned} \frac{x^2}{ \frac{\color{blue}{33x^4+5148x^2+135135}}{\color{blue}{x^4+429x^2+19305}} } & \xlongequal{\text{Step 1}} x^2 \cdot \frac{\color{blue}{x^4+429x^2+19305}}{\color{blue}{33x^4+5148x^2+135135}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{x^2}{\color{red}{1}} \cdot \frac{x^4+429x^2+19305}{33x^4+5148x^2+135135} \xlongequal{\text{Step 3}} \frac{ x^2 \cdot \left( x^4+429x^2+19305 \right) }{ 1 \cdot \left( 33x^4+5148x^2+135135 \right) } = \\[1ex] & \xlongequal{\text{Step 4}} \frac{ x^6+429x^4+19305x^2 }{ 33x^4+5148x^2+135135 } \end{aligned} $$

Add $5$ and $ \dfrac{x^6+429x^4+19305x^2}{33x^4+5148x^2+135135} $ to get $ \dfrac{ \color{purple}{ x^6+594x^4+45045x^2+675675 } }{ 33x^4+5148x^2+135135 }$.

Step 1: Write $ 5 $ 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 $\color{blue}{ 33x^4+5148x^2+135135 }$.

$$ \begin{aligned} 5+ \frac{x^6+429x^4+19305x^2}{33x^4+5148x^2+135135} & \xlongequal{\text{Step 1}} \frac{5}{\color{red}{1}} + \frac{x^6+429x^4+19305x^2}{33x^4+5148x^2+135135} = \\[1ex] &= \frac{ 5 \cdot \color{blue}{ \left( 33x^4+5148x^2+135135 \right) }}{ 1 \cdot \color{blue}{ \left( 33x^4+5148x^2+135135 \right) }} + \frac{ x^6+429x^4+19305x^2 }{ 33x^4+5148x^2+135135 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 165x^4+25740x^2+675675 } }{ 33x^4+5148x^2+135135 } + \frac{ \color{purple}{ x^6+429x^4+19305x^2 } }{ 33x^4+5148x^2+135135 } = \\[1ex] &=\frac{ \color{purple}{ x^6+594x^4+45045x^2+675675 } }{ 33x^4+5148x^2+135135 } \end{aligned} $$

Divide $x^2$ by $ \dfrac{x^6+594x^4+45045x^2+675675}{33x^4+5148x^2+135135} $ to get $ \dfrac{ 33x^6+5148x^4+135135x^2 }{ x^6+594x^4+45045x^2+675675 } $.

Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction.

Step 2: Write $ x^2 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 3: Multiply numerators and denominators.

Step 4: Simplify numerator and denominator.

$$ \begin{aligned} \frac{x^2}{ \frac{\color{blue}{x^6+594x^4+45045x^2+675675}}{\color{blue}{33x^4+5148x^2+135135}} } & \xlongequal{\text{Step 1}} x^2 \cdot \frac{\color{blue}{33x^4+5148x^2+135135}}{\color{blue}{x^6+594x^4+45045x^2+675675}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{x^2}{\color{red}{1}} \cdot \frac{33x^4+5148x^2+135135}{x^6+594x^4+45045x^2+675675} \xlongequal{\text{Step 3}} \frac{ x^2 \cdot \left( 33x^4+5148x^2+135135 \right) }{ 1 \cdot \left( x^6+594x^4+45045x^2+675675 \right) } = \\[1ex] & \xlongequal{\text{Step 4}} \frac{ 33x^6+5148x^4+135135x^2 }{ x^6+594x^4+45045x^2+675675 } \end{aligned} $$

Add $3$ and $ \dfrac{33x^6+5148x^4+135135x^2}{x^6+594x^4+45045x^2+675675} $ to get $ \dfrac{ \color{purple}{ 36x^6+6930x^4+270270x^2+2027025 } }{ x^6+594x^4+45045x^2+675675 }$.

Step 1: Write $ 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 $\color{blue}{ x^6+594x^4+45045x^2+675675 }$.

$$ \begin{aligned} 3+ \frac{33x^6+5148x^4+135135x^2}{x^6+594x^4+45045x^2+675675} & \xlongequal{\text{Step 1}} \frac{3}{\color{red}{1}} + \frac{33x^6+5148x^4+135135x^2}{x^6+594x^4+45045x^2+675675} = \\[1ex] &= \frac{ 3 \cdot \color{blue}{ \left( x^6+594x^4+45045x^2+675675 \right) }}{ 1 \cdot \color{blue}{ \left( x^6+594x^4+45045x^2+675675 \right) }} + \frac{ 33x^6+5148x^4+135135x^2 }{ x^6+594x^4+45045x^2+675675 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 3x^6+1782x^4+135135x^2+2027025 } }{ x^6+594x^4+45045x^2+675675 } + \frac{ \color{purple}{ 33x^6+5148x^4+135135x^2 } }{ x^6+594x^4+45045x^2+675675 } = \\[1ex] &=\frac{ \color{purple}{ 36x^6+6930x^4+270270x^2+2027025 } }{ x^6+594x^4+45045x^2+675675 } \end{aligned} $$

Divide $x^2$ by $ \dfrac{36x^6+6930x^4+270270x^2+2027025}{x^6+594x^4+45045x^2+675675} $ to get $ \dfrac{ x^8+594x^6+45045x^4+675675x^2 }{ 36x^6+6930x^4+270270x^2+2027025 } $.

Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction.

Step 2: Write $ x^2 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 3: Multiply numerators and denominators.

Step 4: Simplify numerator and denominator.

$$ \begin{aligned} \frac{x^2}{ \frac{\color{blue}{36x^6+6930x^4+270270x^2+2027025}}{\color{blue}{x^6+594x^4+45045x^2+675675}} } & \xlongequal{\text{Step 1}} x^2 \cdot \frac{\color{blue}{x^6+594x^4+45045x^2+675675}}{\color{blue}{36x^6+6930x^4+270270x^2+2027025}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{x^2}{\color{red}{1}} \cdot \frac{x^6+594x^4+45045x^2+675675}{36x^6+6930x^4+270270x^2+2027025} = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x^2 \cdot \left( x^6+594x^4+45045x^2+675675 \right) }{ 1 \cdot \left( 36x^6+6930x^4+270270x^2+2027025 \right) } = \\[1ex] & \xlongequal{\text{Step 4}} \frac{ x^8+594x^6+45045x^4+675675x^2 }{ 36x^6+6930x^4+270270x^2+2027025 } \end{aligned} $$

Add $1$ and $ \dfrac{x^8+594x^6+45045x^4+675675x^2}{36x^6+6930x^4+270270x^2+2027025} $ to get $ \dfrac{ \color{purple}{ x^8+630x^6+51975x^4+945945x^2+2027025 } }{ 36x^6+6930x^4+270270x^2+2027025 }$.

Step 1: Write $ 1 $ 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 $\color{blue}{ 36x^6+6930x^4+270270x^2+2027025 }$.

$$ \begin{aligned} 1+ \frac{x^8+594x^6+45045x^4+675675x^2}{36x^6+6930x^4+270270x^2+2027025} & \xlongequal{\text{Step 1}} \frac{1}{\color{red}{1}} + \frac{x^8+594x^6+45045x^4+675675x^2}{36x^6+6930x^4+270270x^2+2027025} = \\[1ex] &= \frac{ 1 \cdot \color{blue}{ \left( 36x^6+6930x^4+270270x^2+2027025 \right) }}{ 1 \cdot \color{blue}{ \left( 36x^6+6930x^4+270270x^2+2027025 \right) }} + \frac{ x^8+594x^6+45045x^4+675675x^2 }{ 36x^6+6930x^4+270270x^2+2027025 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 36x^6+6930x^4+270270x^2+2027025 } }{ 36x^6+6930x^4+270270x^2+2027025 } + \frac{ \color{purple}{ x^8+594x^6+45045x^4+675675x^2 } }{ 36x^6+6930x^4+270270x^2+2027025 } = \\[1ex] &=\frac{ \color{purple}{ x^8+630x^6+51975x^4+945945x^2+2027025 } }{ 36x^6+6930x^4+270270x^2+2027025 } \end{aligned} $$

Divide $x$ by $ \dfrac{x^8+630x^6+51975x^4+945945x^2+2027025}{36x^6+6930x^4+270270x^2+2027025} $ to get $ \dfrac{ 36x^7+6930x^5+270270x^3+2027025x }{ x^8+630x^6+51975x^4+945945x^2+2027025 } $.

Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction.

Step 2: Write $ x $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 3: Multiply numerators and denominators.

Step 4: Simplify numerator and denominator.

$$ \begin{aligned} \frac{x}{ \frac{\color{blue}{x^8+630x^6+51975x^4+945945x^2+2027025}}{\color{blue}{36x^6+6930x^4+270270x^2+2027025}} } & \xlongequal{\text{Step 1}} x \cdot \frac{\color{blue}{36x^6+6930x^4+270270x^2+2027025}}{\color{blue}{x^8+630x^6+51975x^4+945945x^2+2027025}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{x}{\color{red}{1}} \cdot \frac{36x^6+6930x^4+270270x^2+2027025}{x^8+630x^6+51975x^4+945945x^2+2027025} = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x \cdot \left( 36x^6+6930x^4+270270x^2+2027025 \right) }{ 1 \cdot \left( x^8+630x^6+51975x^4+945945x^2+2027025 \right) } = \\[1ex] & \xlongequal{\text{Step 4}} \frac{ 36x^7+6930x^5+270270x^3+2027025x }{ x^8+630x^6+51975x^4+945945x^2+2027025 } \end{aligned} $$