Multiply $ \dfrac{5}{4} $ by $ x^3 $ to get $ \dfrac{ 5x^3 }{ 4 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{5}{4} \cdot x^3 & \xlongequal{\text{Step 1}} \frac{5}{4} \cdot \frac{x^3}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5 \cdot x^3 }{ 4 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5x^3 }{ 4 } \end{aligned} $$

Multiply $ \dfrac{1}{6} $ by $ x $ to get $ \dfrac{ x }{ 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.

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

Multiply $ \dfrac{5x^3}{4} $ by $ y $ to get $ \dfrac{ 5x^3y }{ 4 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{5x^3}{4} \cdot y & \xlongequal{\text{Step 1}} \frac{5x^3}{4} \cdot \frac{y}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5x^3 \cdot y }{ 4 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5x^3y }{ 4 } \end{aligned} $$

Multiply $ \dfrac{x}{6} $ by $ y^2 $ to get $ \dfrac{ xy^2 }{ 6 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{x}{6} \cdot y^2 & \xlongequal{\text{Step 1}} \frac{x}{6} \cdot \frac{y^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ x \cdot y^2 }{ 6 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ xy^2 }{ 6 } \end{aligned} $$

Add $ \dfrac{5x^3y}{4} $ and $ \dfrac{xy^2}{6} $ to get $ \dfrac{ \color{purple}{ 15x^3y+2xy^2 } }{ 12 }$.

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 }$ and the second by $\color{blue}{ 2 }$.

$$ \begin{aligned} \frac{5x^3y}{4} + \frac{xy^2}{6} & = \frac{ 5x^3y \cdot \color{blue}{ 3 }}{ 4 \cdot \color{blue}{ 3 }} + \frac{ xy^2 \cdot \color{blue}{ 2 }}{ 6 \cdot \color{blue}{ 2 }} = \\[1ex] &=\frac{ \color{purple}{ 15x^3y } }{ 12 } + \frac{ \color{purple}{ 2xy^2 } }{ 12 }=\frac{ \color{purple}{ 15x^3y+2xy^2 } }{ 12 } \end{aligned} $$