Multiply $42$ by $ \dfrac{x}{7} $ to get $ \dfrac{ 42x }{ 7 } $.

Step 1: Write $ 42 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 42 \cdot \frac{x}{7} & \xlongequal{\text{Step 1}} \frac{42}{\color{red}{1}} \cdot \frac{x}{7} \xlongequal{\text{Step 2}} \frac{ 42 \cdot x }{ 1 \cdot 7 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 42x }{ 7 } \end{aligned} $$

Add $x-3$ and $ \dfrac{42x}{7} $ to get $ \dfrac{ \color{purple}{ 49x-21 } }{ 7 }$.

Step 1: Write $ x-3 $ 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 $\color{blue}{ 7 }$.

$$ \begin{aligned} x-3+ \frac{42x}{7} & \xlongequal{\text{Step 1}} \frac{x-3}{\color{red}{1}} + \frac{42x}{7} = \frac{ \left( x-3 \right) \cdot \color{blue}{ 7 }}{ 1 \cdot \color{blue}{ 7 }} + \frac{ 42x }{ 7 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 7x-21 } }{ 7 } + \frac{ \color{purple}{ 42x } }{ 7 }=\frac{ \color{purple}{ 49x-21 } }{ 7 } \end{aligned} $$