Multiply $10$ by $ \dfrac{x}{14x^2+6} $ to get $ \dfrac{ 10x }{ 14x^2+6 } $.

Step 1: Write $ 10 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 10 \cdot \frac{x}{14x^2+6} & \xlongequal{\text{Step 1}} \frac{10}{\color{red}{1}} \cdot \frac{x}{14x^2+6} \xlongequal{\text{Step 2}} \frac{ 10 \cdot x }{ 1 \cdot \left( 14x^2+6 \right) } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 10x }{ 14x^2+6 } \end{aligned} $$

Multiply $16$ by $ \dfrac{x}{8x} $ to get $ \dfrac{ 16x }{ 8x } $.

Step 1: Write $ 16 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 16 \cdot \frac{x}{8x} & \xlongequal{\text{Step 1}} \frac{16}{\color{red}{1}} \cdot \frac{x}{8x} \xlongequal{\text{Step 2}} \frac{ 16 \cdot x }{ 1 \cdot 8x } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 16x }{ 8x } \end{aligned} $$

Add $ \dfrac{10x}{14x^2+6} $ and $ \dfrac{16x}{8x} $ to get $ \dfrac{ \color{purple}{ 224x^3+80x^2+96x } }{ 112x^3+48x }$.

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}{ 8x }$ and the second by $\color{blue}{ 14x^2+6 }$.

$$ \begin{aligned} \frac{10x}{14x^2+6} + \frac{16x}{8x} & = \frac{ 10x \cdot \color{blue}{ 8x }}{ \left( 14x^2+6 \right) \cdot \color{blue}{ 8x }} + \frac{ 16x \cdot \color{blue}{ \left( 14x^2+6 \right) }}{ 8x \cdot \color{blue}{ \left( 14x^2+6 \right) }} = \\[1ex] &=\frac{ \color{purple}{ 80x^2 } }{ 112x^3+48x } + \frac{ \color{purple}{ 224x^3+96x } }{ 112x^3+48x }=\frac{ \color{purple}{ 224x^3+80x^2+96x } }{ 112x^3+48x } \end{aligned} $$