Divide $ \dfrac{x}{6} $ by $ x $ to get $ \dfrac{1}{6} $.

Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction.

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

Step 3: Multiply numerators and denominators.

$$ \begin{aligned} \frac{ \frac{x}{6} }{x} & \xlongequal{\text{Step 1}} \frac{x}{6} \cdot \frac{\color{blue}{1}}{\color{blue}{x}} \xlongequal{\text{Step 2}} \frac{\color{blue}{1}}{6} \cdot \frac{1}{\color{blue}{1}} = \\[1ex] &= \frac{1}{6} \end{aligned} $$

Multiply $ \dfrac{14}{5} $ by $ \dfrac{1}{6} $ to get $ \dfrac{7}{15} $.

Multiply numerators and denominators.

Step 2: Cancel down by $ \color{blue}{2} $

$$ \begin{aligned} \frac{14}{5} \cdot \frac{1}{6} = \frac{14 : \color{blue}{2}}{30 : \color{blue}{2}}= \frac{7}{15} \end{aligned} $$

Add $7x$ and $ \dfrac{7}{15} $ to get $ \dfrac{ \color{purple}{ 105x+7 } }{ 15 }$.

Step 1: Write $ 7x $ 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 $\color{blue}{ 15 }$.

$$ \begin{aligned} 7x+ \frac{7}{15} & \xlongequal{\text{Step 1}} \frac{7x}{\color{red}{1}} + \frac{7}{15} = \frac{ 7x \cdot \color{blue}{ 15 }}{ 1 \cdot \color{blue}{ 15 }} + \frac{ 7 }{ 15 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 105x } }{ 15 } + \frac{ \color{purple}{ 7 } }{ 15 }=\frac{ \color{purple}{ 105x+7 } }{ 15 } \end{aligned} $$

Add $ \dfrac{105x+7}{15} $ and $ 4 $ to get $ \dfrac{ \color{purple}{ 105x+67 } }{ 15 }$.

Step 1: Write $ 4 $ 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 $\color{blue}{15}$.

$$ \begin{aligned} \frac{105x+7}{15} +4 & \xlongequal{\text{Step 1}} \frac{105x+7}{15} + \frac{4}{\color{red}{1}} = \frac{ 105x+7 }{ 15 } + \frac{ 4 \cdot \color{blue}{ 15 }}{ 1 \cdot \color{blue}{ 15 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 105x+7 } }{ 15 } + \frac{ \color{purple}{ 60 } }{ 15 }=\frac{ \color{purple}{ 105x+67 } }{ 15 } \end{aligned} $$