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 $ \dfrac{3x}{5} $ by $ x $ to get $ \dfrac{ 3x^2 }{ 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.

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

Add $x^2$ and $ \dfrac{3x^2}{5} $ to get $ \dfrac{ \color{purple}{ 8x^2 } }{ 5 }$.

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

Step 2: To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 5 }$.

$$ \begin{aligned} x^2+ \frac{3x^2}{5} & \xlongequal{\text{Step 1}} \frac{x^2}{\color{red}{1}} + \frac{3x^2}{5} = \frac{ x^2 \cdot \color{blue}{ 5 }}{ 1 \cdot \color{blue}{ 5 }} + \frac{ 3x^2 }{ 5 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 5x^2 } }{ 5 } + \frac{ \color{purple}{ 3x^2 } }{ 5 }=\frac{ \color{purple}{ 8x^2 } }{ 5 } \end{aligned} $$