Add $ \dfrac{3}{n-5} $ and $ \dfrac{6}{3n-8} $ to get $ \dfrac{ \color{purple}{ 15n-54 } }{ 3n^2-23n+40 }$.

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}{ 3n-8 }$ and the second by $\color{blue}{ n-5 }$.

$$ \begin{aligned} \frac{3}{n-5} + \frac{6}{3n-8} & = \frac{ 3 \cdot \color{blue}{ \left( 3n-8 \right) }}{ \left( n-5 \right) \cdot \color{blue}{ \left( 3n-8 \right) }} + \frac{ 6 \cdot \color{blue}{ \left( n-5 \right) }}{ \left( 3n-8 \right) \cdot \color{blue}{ \left( n-5 \right) }} = \\[1ex] &=\frac{ \color{purple}{ 9n-24 } }{ 3n^2-8n-15n+40 } + \frac{ \color{purple}{ 6n-30 } }{ 3n^2-8n-15n+40 } = \\[1ex] &=\frac{ \color{purple}{ 15n-54 } }{ 3n^2-23n+40 } \end{aligned} $$