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

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

Step 2: Cancel $ \color{blue}{ x } $ in first and second fraction.

Step 3: Multiply numerators and denominators.

Step 4: Simplify numerator and denominator.

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