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

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.

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

Multiply $ \dfrac{3}{10} $ by $ x $ to get $ \dfrac{ 3x }{ 10 } $.

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.

$$ \begin{aligned} \frac{3}{10} \cdot x & \xlongequal{\text{Step 1}} \frac{3}{10} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 3 \cdot x }{ 10 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3x }{ 10 } \end{aligned} $$

Add $ \dfrac{4x}{5} $ and $ \dfrac{3}{8} $ to get $ \dfrac{ \color{purple}{ 32x+15 } }{ 40 }$.

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}{ 8 }$ and the second by $\color{blue}{ 5 }$.

$$ \begin{aligned} \frac{4x}{5} + \frac{3}{8} & = \frac{ 4x \cdot \color{blue}{ 8 }}{ 5 \cdot \color{blue}{ 8 }} + \frac{ 3 \cdot \color{blue}{ 5 }}{ 8 \cdot \color{blue}{ 5 }} = \\[1ex] &=\frac{ \color{purple}{ 32x } }{ 40 } + \frac{ \color{purple}{ 15 } }{ 40 }=\frac{ \color{purple}{ 32x+15 } }{ 40 } \end{aligned} $$

Multiply $ \dfrac{3}{10} $ by $ x $ to get $ \dfrac{ 3x }{ 10 } $.

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.

$$ \begin{aligned} \frac{3}{10} \cdot x & \xlongequal{\text{Step 1}} \frac{3}{10} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 3 \cdot x }{ 10 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3x }{ 10 } \end{aligned} $$

Add $ \dfrac{32x+15}{40} $ and $ \dfrac{3x}{10} $ to get $ \dfrac{ \color{purple}{ 44x+15 } }{ 40 }$.

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

$$ \begin{aligned} \frac{32x+15}{40} + \frac{3x}{10} & = \frac{ 32x+15 }{ 40 } + \frac{ 3x \cdot \color{blue}{ 4 }}{ 10 \cdot \color{blue}{ 4 }} = \\[1ex] &=\frac{ \color{purple}{ 32x+15 } }{ 40 } + \frac{ \color{purple}{ 12x } }{ 40 }=\frac{ \color{purple}{ 44x+15 } }{ 40 } \end{aligned} $$