Multiply $ \dfrac{3}{m^2} $ by $ \dfrac{16}{m} $ to get $ \dfrac{ 48 }{ m^3 } $.

Step 1: Multiply numerators and denominators.

Step 2: Simplify numerator and denominator.

$$ \begin{aligned} \frac{3}{m^2} \cdot \frac{16}{m} \xlongequal{\text{Step 1}} \frac{ 3 \cdot 16 }{ m^2 \cdot m } \xlongequal{\text{Step 2}} \frac{ 48 }{ m^3 } \end{aligned} $$

Add $ \dfrac{4}{m} $ and $ \dfrac{48}{m^3} $ to get $ \dfrac{ \color{purple}{ 4m^3+48m } }{ m^4 }$.

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}{ m^3 }$ and the second by $\color{blue}{ m }$.

$$ \begin{aligned} \frac{4}{m} + \frac{48}{m^3} & = \frac{ 4 \cdot \color{blue}{ m^3 }}{ m \cdot \color{blue}{ m^3 }} + \frac{ 48 \cdot \color{blue}{ m }}{ m^3 \cdot \color{blue}{ m }} = \\[1ex] &=\frac{ \color{purple}{ 4m^3 } }{ m^4 } + \frac{ \color{purple}{ 48m } }{ m^4 }=\frac{ \color{purple}{ 4m^3+48m } }{ m^4 } \end{aligned} $$

Add $ \dfrac{4m^3+48m}{m^4} $ and $ 12m^2 $ to get $ \dfrac{ \color{purple}{ 12m^6+4m^3+48m } }{ m^4 }$.

Step 1: Write $ 12m^2 $ 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 $\color{blue}{m^4}$.

$$ \begin{aligned} \frac{4m^3+48m}{m^4} +12m^2 & \xlongequal{\text{Step 1}} \frac{4m^3+48m}{m^4} + \frac{12m^2}{\color{red}{1}} = \frac{ 4m^3+48m }{ m^4 } + \frac{ 12m^2 \cdot \color{blue}{ m^4 }}{ 1 \cdot \color{blue}{ m^4 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 4m^3+48m } }{ m^4 } + \frac{ \color{purple}{ 12m^6 } }{ m^4 }=\frac{ \color{purple}{ 12m^6+4m^3+48m } }{ m^4 } \end{aligned} $$