Add $ \dfrac{3}{x+2} $ and $ \dfrac{4}{x-7} $ to get $ \dfrac{ \color{purple}{ 7x-13 } }{ x^2-5x-14 }$.

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}{ x-7 }$ and the second by $\color{blue}{ x+2 }$.

$$ \begin{aligned} \frac{3}{x+2} + \frac{4}{x-7} & = \frac{ 3 \cdot \color{blue}{ \left( x-7 \right) }}{ \left( x+2 \right) \cdot \color{blue}{ \left( x-7 \right) }} + \frac{ 4 \cdot \color{blue}{ \left( x+2 \right) }}{ \left( x-7 \right) \cdot \color{blue}{ \left( x+2 \right) }} = \\[1ex] &=\frac{ \color{purple}{ 3x-21 } }{ x^2-7x+2x-14 } + \frac{ \color{purple}{ 4x+8 } }{ x^2-7x+2x-14 }=\frac{ \color{purple}{ 7x-13 } }{ x^2-5x-14 } \end{aligned} $$