Simplify $ \dfrac{4x+6}{4x^2-9} $ to $ \dfrac{2}{2x-3} $.

Factor both the denominator and the numerator, then cancel the common factor. $\color{blue}{2x+3}$.

$$ \begin{aligned} \frac{4x+6}{4x^2-9} & =\frac{ 2 \cdot \color{blue}{ \left( 2x+3 \right) }}{ \left( 2x-3 \right) \cdot \color{blue}{ \left( 2x+3 \right) }} = \\[1ex] &= \frac{2}{2x-3} \end{aligned} $$

Add $ \dfrac{2}{2x-3} $ and $ \dfrac{4}{2x-3} $ to get $ \dfrac{6}{2x-3} $.

To add expressions with the same denominators, we add the numerators and write the result over the common denominator.

$$ \begin{aligned} \frac{2}{2x-3} + \frac{4}{2x-3} & = \frac{2}{\color{blue}{2x-3}} + \frac{4}{\color{blue}{2x-3}} =\frac{ 2 + 4 }{ \color{blue}{ 2x-3 }} = \\[1ex] &= \frac{6}{2x-3} \end{aligned} $$