Add $ \dfrac{x+2}{x^2-9} $ and $ \dfrac{3}{x-3} $ to get $ \dfrac{ \color{purple}{ 4x+11 } }{ x^2-9 }$.

To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{x+3}$.

$$ \begin{aligned} \frac{x+2}{x^2-9} + \frac{3}{x-3} & = \frac{ x+2 }{ x^2-9 } + \frac{ 3 \cdot \color{blue}{ \left( x+3 \right) }}{ \left( x-3 \right) \cdot \color{blue}{ \left( x+3 \right) }} = \\[1ex] &=\frac{ \color{purple}{ x+2 } }{ x^2-9 } + \frac{ \color{purple}{ 3x+9 } }{ x^2-9 }=\frac{ \color{purple}{ 4x+11 } }{ x^2-9 } \end{aligned} $$