Add $ \dfrac{3}{b-8} $ and $ \dfrac{7}{b+3} $ to get $ \dfrac{ \color{purple}{ 10b-47 } }{ b^2-5b-24 }$.

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}{ b+3 }$ and the second by $\color{blue}{ b-8 }$.

$$ \begin{aligned} \frac{3}{b-8} + \frac{7}{b+3} & = \frac{ 3 \cdot \color{blue}{ \left( b+3 \right) }}{ \left( b-8 \right) \cdot \color{blue}{ \left( b+3 \right) }} + \frac{ 7 \cdot \color{blue}{ \left( b-8 \right) }}{ \left( b+3 \right) \cdot \color{blue}{ \left( b-8 \right) }} = \\[1ex] &=\frac{ \color{purple}{ 3b+9 } }{ b^2+3b-8b-24 } + \frac{ \color{purple}{ 7b-56 } }{ b^2+3b-8b-24 }=\frac{ \color{purple}{ 10b-47 } }{ b^2-5b-24 } \end{aligned} $$