Add $ \dfrac{1}{3} $ and $ \dfrac{x^2}{36} $ to get $ \dfrac{ \color{purple}{ x^2+12 } }{ 36 }$.

To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 12 }$.

$$ \begin{aligned} \frac{1}{3} + \frac{x^2}{36} & = \frac{ 1 \cdot \color{blue}{ 12 }}{ 3 \cdot \color{blue}{ 12 }} + \frac{ x^2 }{ 36 } = \\[1ex] &=\frac{ \color{purple}{ 12 } }{ 36 } + \frac{ \color{purple}{ x^2 } }{ 36 }=\frac{ \color{purple}{ x^2+12 } }{ 36 } \end{aligned} $$

Divide $ \dfrac{x^2+12}{36} $ by $ x $ to get $ \dfrac{ x^2+12 }{ 36x } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{ \frac{x^2+12}{36} }{x} & \xlongequal{\text{Step 1}} \frac{x^2+12}{36} \cdot \frac{\color{blue}{1}}{\color{blue}{x}} \xlongequal{\text{Step 2}} \frac{ \left( x^2+12 \right) \cdot 1 }{ 36 \cdot x } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x^2+12 }{ 36x } \end{aligned} $$