Add $ \dfrac{x-4}{3x^2+x-4} $ and $ \dfrac{8}{5} $ to get $ \dfrac{ \color{purple}{ 24x^2+13x-52 } }{ 15x^2+5x-20 }$.

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}{ 5 }$ and the second by $\color{blue}{ 3x^2+x-4 }$.

$$ \begin{aligned} \frac{x-4}{3x^2+x-4} + \frac{8}{5} & = \frac{ \left( x-4 \right) \cdot \color{blue}{ 5 }}{ \left( 3x^2+x-4 \right) \cdot \color{blue}{ 5 }} + \frac{ 8 \cdot \color{blue}{ \left( 3x^2+x-4 \right) }}{ 5 \cdot \color{blue}{ \left( 3x^2+x-4 \right) }} = \\[1ex] &=\frac{ \color{purple}{ 5x-20 } }{ 15x^2+5x-20 } + \frac{ \color{purple}{ 24x^2+8x-32 } }{ 15x^2+5x-20 } = \\[1ex] &=\frac{ \color{purple}{ 24x^2+13x-52 } }{ 15x^2+5x-20 } \end{aligned} $$