$$ 8 x \cdot 7 m^2 = 56 m^{2} x $$

Add $ \dfrac{1}{m} $ and $ 56m^2x $ to get $ \dfrac{ \color{purple}{ 56m^3x+1 } }{ m }$.

Step 1: Write $ 56m^2x $ 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 $\color{blue}{m}$.

$$ \begin{aligned} \frac{1}{m} +56m^2x & \xlongequal{\text{Step 1}} \frac{1}{m} + \frac{56m^2x}{\color{red}{1}} = \frac{ 1 }{ m } + \frac{ 56m^2x \cdot \color{blue}{ m }}{ 1 \cdot \color{blue}{ m }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 1 } }{ m } + \frac{ \color{purple}{ 56m^3x } }{ m }=\frac{ \color{purple}{ 56m^3x+1 } }{ m } \end{aligned} $$

Multiply $56$ by $ \dfrac{m}{7} $ to get $ \dfrac{ 56m }{ 7 } $.

Step 1: Write $ 56 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 56 \cdot \frac{m}{7} & \xlongequal{\text{Step 1}} \frac{56}{\color{red}{1}} \cdot \frac{m}{7} \xlongequal{\text{Step 2}} \frac{ 56 \cdot m }{ 1 \cdot 7 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 56m }{ 7 } \end{aligned} $$

Add $ \dfrac{56m^3x+1}{m} $ and $ \dfrac{56m}{7} $ to get $ \dfrac{ \color{purple}{ 392m^3x+56m^2+7 } }{ 7m }$.

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 }$ and the second by $\color{blue}{ m }$.

$$ \begin{aligned} \frac{56m^3x+1}{m} + \frac{56m}{7} & = \frac{ \left( 56m^3x+1 \right) \cdot \color{blue}{ 7 }}{ m \cdot \color{blue}{ 7 }} + \frac{ 56m \cdot \color{blue}{ m }}{ 7 \cdot \color{blue}{ m }} = \\[1ex] &=\frac{ \color{purple}{ 392m^3x+7 } }{ 7m } + \frac{ \color{purple}{ 56m^2 } }{ 7m }=\frac{ \color{purple}{ 392m^3x+56m^2+7 } }{ 7m } \end{aligned} $$