Add $11$ and $ \dfrac{x^2}{13} $ to get $ \dfrac{ \color{purple}{ x^2+143 } }{ 13 }$.

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 $\color{blue}{ 13 }$.

$$ \begin{aligned} 11+ \frac{x^2}{13} & \xlongequal{\text{Step 1}} \frac{11}{\color{red}{1}} + \frac{x^2}{13} = \frac{ 11 \cdot \color{blue}{ 13 }}{ 1 \cdot \color{blue}{ 13 }} + \frac{ x^2 }{ 13 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 143 } }{ 13 } + \frac{ \color{purple}{ x^2 } }{ 13 }=\frac{ \color{purple}{ x^2+143 } }{ 13 } \end{aligned} $$

Divide $x^2$ by $ \dfrac{x^2+143}{13} $ to get $ \dfrac{ 13x^2 }{ x^2+143 } $.

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.

$$ \begin{aligned} \frac{x^2}{ \frac{\color{blue}{x^2+143}}{\color{blue}{13}} } & \xlongequal{\text{Step 1}} x^2 \cdot \frac{\color{blue}{13}}{\color{blue}{x^2+143}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{x^2}{\color{red}{1}} \cdot \frac{13}{x^2+143} \xlongequal{\text{Step 3}} \frac{ x^2 \cdot 13 }{ 1 \cdot \left( x^2+143 \right) } = \\[1ex] & \xlongequal{\text{Step 4}} \frac{ 13x^2 }{ x^2+143 } \end{aligned} $$

Add $9$ and $ \dfrac{13x^2}{x^2+143} $ to get $ \dfrac{ \color{purple}{ 22x^2+1287 } }{ x^2+143 }$.

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 $\color{blue}{ x^2+143 }$.

$$ \begin{aligned} 9+ \frac{13x^2}{x^2+143} & \xlongequal{\text{Step 1}} \frac{9}{\color{red}{1}} + \frac{13x^2}{x^2+143} = \frac{ 9 \cdot \color{blue}{ \left( x^2+143 \right) }}{ 1 \cdot \color{blue}{ \left( x^2+143 \right) }} + \frac{ 13x^2 }{ x^2+143 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 9x^2+1287 } }{ x^2+143 } + \frac{ \color{purple}{ 13x^2 } }{ x^2+143 }=\frac{ \color{purple}{ 22x^2+1287 } }{ x^2+143 } \end{aligned} $$

Divide $x^2$ by $ \dfrac{22x^2+1287}{x^2+143} $ to get $ \dfrac{ x^4+143x^2 }{ 22x^2+1287 } $.

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.

$$ \begin{aligned} \frac{x^2}{ \frac{\color{blue}{22x^2+1287}}{\color{blue}{x^2+143}} } & \xlongequal{\text{Step 1}} x^2 \cdot \frac{\color{blue}{x^2+143}}{\color{blue}{22x^2+1287}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{x^2}{\color{red}{1}} \cdot \frac{x^2+143}{22x^2+1287} \xlongequal{\text{Step 3}} \frac{ x^2 \cdot \left( x^2+143 \right) }{ 1 \cdot \left( 22x^2+1287 \right) } = \\[1ex] & \xlongequal{\text{Step 4}} \frac{ x^4+143x^2 }{ 22x^2+1287 } \end{aligned} $$

Add $7$ and $ \dfrac{x^4+143x^2}{22x^2+1287} $ to get $ \dfrac{ \color{purple}{ x^4+297x^2+9009 } }{ 22x^2+1287 }$.

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 $\color{blue}{ 22x^2+1287 }$.

$$ \begin{aligned} 7+ \frac{x^4+143x^2}{22x^2+1287} & \xlongequal{\text{Step 1}} \frac{7}{\color{red}{1}} + \frac{x^4+143x^2}{22x^2+1287} = \frac{ 7 \cdot \color{blue}{ \left( 22x^2+1287 \right) }}{ 1 \cdot \color{blue}{ \left( 22x^2+1287 \right) }} + \frac{ x^4+143x^2 }{ 22x^2+1287 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 154x^2+9009 } }{ 22x^2+1287 } + \frac{ \color{purple}{ x^4+143x^2 } }{ 22x^2+1287 } = \\[1ex] &=\frac{ \color{purple}{ x^4+297x^2+9009 } }{ 22x^2+1287 } \end{aligned} $$

Divide $x^2$ by $ \dfrac{x^4+297x^2+9009}{22x^2+1287} $ to get $ \dfrac{ 22x^4+1287x^2 }{ x^4+297x^2+9009 } $.

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.

$$ \begin{aligned} \frac{x^2}{ \frac{\color{blue}{x^4+297x^2+9009}}{\color{blue}{22x^2+1287}} } & \xlongequal{\text{Step 1}} x^2 \cdot \frac{\color{blue}{22x^2+1287}}{\color{blue}{x^4+297x^2+9009}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{x^2}{\color{red}{1}} \cdot \frac{22x^2+1287}{x^4+297x^2+9009} \xlongequal{\text{Step 3}} \frac{ x^2 \cdot \left( 22x^2+1287 \right) }{ 1 \cdot \left( x^4+297x^2+9009 \right) } = \\[1ex] & \xlongequal{\text{Step 4}} \frac{ 22x^4+1287x^2 }{ x^4+297x^2+9009 } \end{aligned} $$

Add $5$ and $ \dfrac{22x^4+1287x^2}{x^4+297x^2+9009} $ to get $ \dfrac{ \color{purple}{ 27x^4+2772x^2+45045 } }{ x^4+297x^2+9009 }$.

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 $\color{blue}{ x^4+297x^2+9009 }$.

$$ \begin{aligned} 5+ \frac{22x^4+1287x^2}{x^4+297x^2+9009} & \xlongequal{\text{Step 1}} \frac{5}{\color{red}{1}} + \frac{22x^4+1287x^2}{x^4+297x^2+9009} = \\[1ex] &= \frac{ 5 \cdot \color{blue}{ \left( x^4+297x^2+9009 \right) }}{ 1 \cdot \color{blue}{ \left( x^4+297x^2+9009 \right) }} + \frac{ 22x^4+1287x^2 }{ x^4+297x^2+9009 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 5x^4+1485x^2+45045 } }{ x^4+297x^2+9009 } + \frac{ \color{purple}{ 22x^4+1287x^2 } }{ x^4+297x^2+9009 } = \\[1ex] &=\frac{ \color{purple}{ 27x^4+2772x^2+45045 } }{ x^4+297x^2+9009 } \end{aligned} $$

Divide $x^2$ by $ \dfrac{27x^4+2772x^2+45045}{x^4+297x^2+9009} $ to get $ \dfrac{ x^6+297x^4+9009x^2 }{ 27x^4+2772x^2+45045 } $.

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.

$$ \begin{aligned} \frac{x^2}{ \frac{\color{blue}{27x^4+2772x^2+45045}}{\color{blue}{x^4+297x^2+9009}} } & \xlongequal{\text{Step 1}} x^2 \cdot \frac{\color{blue}{x^4+297x^2+9009}}{\color{blue}{27x^4+2772x^2+45045}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{x^2}{\color{red}{1}} \cdot \frac{x^4+297x^2+9009}{27x^4+2772x^2+45045} \xlongequal{\text{Step 3}} \frac{ x^2 \cdot \left( x^4+297x^2+9009 \right) }{ 1 \cdot \left( 27x^4+2772x^2+45045 \right) } = \\[1ex] & \xlongequal{\text{Step 4}} \frac{ x^6+297x^4+9009x^2 }{ 27x^4+2772x^2+45045 } \end{aligned} $$

Add $3$ and $ \dfrac{x^6+297x^4+9009x^2}{27x^4+2772x^2+45045} $ to get $ \dfrac{ \color{purple}{ x^6+378x^4+17325x^2+135135 } }{ 27x^4+2772x^2+45045 }$.

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 $\color{blue}{ 27x^4+2772x^2+45045 }$.

$$ \begin{aligned} 3+ \frac{x^6+297x^4+9009x^2}{27x^4+2772x^2+45045} & \xlongequal{\text{Step 1}} \frac{3}{\color{red}{1}} + \frac{x^6+297x^4+9009x^2}{27x^4+2772x^2+45045} = \\[1ex] &= \frac{ 3 \cdot \color{blue}{ \left( 27x^4+2772x^2+45045 \right) }}{ 1 \cdot \color{blue}{ \left( 27x^4+2772x^2+45045 \right) }} + \frac{ x^6+297x^4+9009x^2 }{ 27x^4+2772x^2+45045 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 81x^4+8316x^2+135135 } }{ 27x^4+2772x^2+45045 } + \frac{ \color{purple}{ x^6+297x^4+9009x^2 } }{ 27x^4+2772x^2+45045 } = \\[1ex] &=\frac{ \color{purple}{ x^6+378x^4+17325x^2+135135 } }{ 27x^4+2772x^2+45045 } \end{aligned} $$

Divide $x^2$ by $ \dfrac{x^6+378x^4+17325x^2+135135}{27x^4+2772x^2+45045} $ to get $ \dfrac{ 27x^6+2772x^4+45045x^2 }{ x^6+378x^4+17325x^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.

$$ \begin{aligned} \frac{x^2}{ \frac{\color{blue}{x^6+378x^4+17325x^2+135135}}{\color{blue}{27x^4+2772x^2+45045}} } & \xlongequal{\text{Step 1}} x^2 \cdot \frac{\color{blue}{27x^4+2772x^2+45045}}{\color{blue}{x^6+378x^4+17325x^2+135135}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{x^2}{\color{red}{1}} \cdot \frac{27x^4+2772x^2+45045}{x^6+378x^4+17325x^2+135135} \xlongequal{\text{Step 3}} \frac{ x^2 \cdot \left( 27x^4+2772x^2+45045 \right) }{ 1 \cdot \left( x^6+378x^4+17325x^2+135135 \right) } = \\[1ex] & \xlongequal{\text{Step 4}} \frac{ 27x^6+2772x^4+45045x^2 }{ x^6+378x^4+17325x^2+135135 } \end{aligned} $$

Add $1$ and $ \dfrac{27x^6+2772x^4+45045x^2}{x^6+378x^4+17325x^2+135135} $ to get $ \dfrac{ \color{purple}{ 28x^6+3150x^4+62370x^2+135135 } }{ x^6+378x^4+17325x^2+135135 }$.

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 $\color{blue}{ x^6+378x^4+17325x^2+135135 }$.

$$ \begin{aligned} 1+ \frac{27x^6+2772x^4+45045x^2}{x^6+378x^4+17325x^2+135135} & \xlongequal{\text{Step 1}} \frac{1}{\color{red}{1}} + \frac{27x^6+2772x^4+45045x^2}{x^6+378x^4+17325x^2+135135} = \\[1ex] &= \frac{ 1 \cdot \color{blue}{ \left( x^6+378x^4+17325x^2+135135 \right) }}{ 1 \cdot \color{blue}{ \left( x^6+378x^4+17325x^2+135135 \right) }} + \frac{ 27x^6+2772x^4+45045x^2 }{ x^6+378x^4+17325x^2+135135 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ x^6+378x^4+17325x^2+135135 } }{ x^6+378x^4+17325x^2+135135 } + \frac{ \color{purple}{ 27x^6+2772x^4+45045x^2 } }{ x^6+378x^4+17325x^2+135135 } = \\[1ex] &=\frac{ \color{purple}{ 28x^6+3150x^4+62370x^2+135135 } }{ x^6+378x^4+17325x^2+135135 } \end{aligned} $$

Divide $x$ by $ \dfrac{28x^6+3150x^4+62370x^2+135135}{x^6+378x^4+17325x^2+135135} $ to get $ \dfrac{ x^7+378x^5+17325x^3+135135x }{ 28x^6+3150x^4+62370x^2+135135 } $.

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.

$$ \begin{aligned} \frac{x}{ \frac{\color{blue}{28x^6+3150x^4+62370x^2+135135}}{\color{blue}{x^6+378x^4+17325x^2+135135}} } & \xlongequal{\text{Step 1}} x \cdot \frac{\color{blue}{x^6+378x^4+17325x^2+135135}}{\color{blue}{28x^6+3150x^4+62370x^2+135135}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{x}{\color{red}{1}} \cdot \frac{x^6+378x^4+17325x^2+135135}{28x^6+3150x^4+62370x^2+135135} \xlongequal{\text{Step 3}} \frac{ x \cdot \left( x^6+378x^4+17325x^2+135135 \right) }{ 1 \cdot \left( 28x^6+3150x^4+62370x^2+135135 \right) } = \\[1ex] & \xlongequal{\text{Step 4}} \frac{ x^7+378x^5+17325x^3+135135x }{ 28x^6+3150x^4+62370x^2+135135 } \end{aligned} $$