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

Step 1: Write $ 5 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Multiply $2$ by $ \dfrac{x}{4x+6} $ to get $ \dfrac{ 2x }{ 4x+6 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

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

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

Multiply $2$ by $ \dfrac{x}{4x+6} $ to get $ \dfrac{ 2x }{ 4x+6 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Subtract $ \dfrac{2x}{4x+6} $ from $ \dfrac{5x^4}{4} $ to get $ \dfrac{ \color{purple}{ 20x^5+30x^4-8x } }{ 16x+24 }$.

To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $ \color{blue}{ 4x+6 }$ and the second by $\color{blue}{ 4 }$.

$$ \begin{aligned} \frac{5x^4}{4} - \frac{2x}{4x+6} & = \frac{ 5x^4 \cdot \color{blue}{ \left( 4x+6 \right) }}{ 4 \cdot \color{blue}{ \left( 4x+6 \right) }} - \frac{ 2x \cdot \color{blue}{ 4 }}{ \left( 4x+6 \right) \cdot \color{blue}{ 4 }} = \\[1ex] &=\frac{ \color{purple}{ 20x^5+30x^4 } }{ 16x+24 } - \frac{ \color{purple}{ 8x } }{ 16x+24 }=\frac{ \color{purple}{ 20x^5+30x^4-8x } }{ 16x+24 } \end{aligned} $$