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

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Multiply $2$ by $ \dfrac{y}{7} $ to get $ \dfrac{ 2y }{ 7 } $.

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.

$$ \begin{aligned} 2 \cdot \frac{y}{7} & \xlongequal{\text{Step 1}} \frac{2}{\color{red}{1}} \cdot \frac{y}{7} \xlongequal{\text{Step 2}} \frac{ 2 \cdot y }{ 1 \cdot 7 } \xlongequal{\text{Step 3}} \frac{ 2y }{ 7 } \end{aligned} $$

Add $ \dfrac{3x}{5} $ and $ \dfrac{2y}{7} $ to get $ \dfrac{ \color{purple}{ 21x+10y } }{ 35 }$.

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

$$ \begin{aligned} \frac{3x}{5} + \frac{2y}{7} & = \frac{ 3x \cdot \color{blue}{ 7 }}{ 5 \cdot \color{blue}{ 7 }} + \frac{ 2y \cdot \color{blue}{ 5 }}{ 7 \cdot \color{blue}{ 5 }} = \\[1ex] &=\frac{ \color{purple}{ 21x } }{ 35 } + \frac{ \color{purple}{ 10y } }{ 35 }=\frac{ \color{purple}{ 21x+10y } }{ 35 } \end{aligned} $$