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

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Multiply $ \dfrac{5}{6} $ by $ x $ to get $ \dfrac{ 5x }{ 6 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{5}{6} \cdot x & \xlongequal{\text{Step 1}} \frac{5}{6} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5 \cdot x }{ 6 \cdot 1 } \xlongequal{\text{Step 3}} \frac{ 5x }{ 6 } \end{aligned} $$

Add $ \dfrac{3x^2}{2} $ and $ \dfrac{5x}{6} $ to get $ \dfrac{ \color{purple}{ 9x^2+5x } }{ 6 }$.

To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 3 }$.

$$ \begin{aligned} \frac{3x^2}{2} + \frac{5x}{6} & = \frac{ 3x^2 \cdot \color{blue}{ 3 }}{ 2 \cdot \color{blue}{ 3 }} + \frac{ 5x }{ 6 } = \\[1ex] &=\frac{ \color{purple}{ 9x^2 } }{ 6 } + \frac{ \color{purple}{ 5x } }{ 6 }=\frac{ \color{purple}{ 9x^2+5x } }{ 6 } \end{aligned} $$