Use the distributive property.

Combine like terms

Multiply $ \dfrac{42}{5} $ by $ x $ to get $ \dfrac{ 42x }{ 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.

$$ \begin{aligned} \frac{42}{5} \cdot x & \xlongequal{\text{Step 1}} \frac{42}{5} \cdot \frac{x}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 42 \cdot x }{ 5 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 42x }{ 5 } \end{aligned} $$

Add $ \dfrac{42x}{5} $ and $ 45 $ to get $ \dfrac{ \color{purple}{ 42x+225 } }{ 5 }$.

Step 1: Write $ 45 $ 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 second fraction by $\color{blue}{5}$.

$$ \begin{aligned} \frac{42x}{5} +45 & \xlongequal{\text{Step 1}} \frac{42x}{5} + \frac{45}{\color{red}{1}} = \frac{ 42x }{ 5 } + \frac{ 45 \cdot \color{blue}{ 5 }}{ 1 \cdot \color{blue}{ 5 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 42x } }{ 5 } + \frac{ \color{purple}{ 225 } }{ 5 }=\frac{ \color{purple}{ 42x+225 } }{ 5 } \end{aligned} $$