Add $ \dfrac{16x^2}{x+3} $ and $ \dfrac{4x^5-36x^4}{x^2-2x-64} $ to get $ \dfrac{ \color{purple}{ 4x^6-24x^5-92x^4-32x^3-1024x^2 } }{ x^3+x^2-70x-192 }$.

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^2-2x-64 }$ and the second by $\color{blue}{ x+3 }$.

$$ \begin{aligned} \frac{16x^2}{x+3} + \frac{4x^5-36x^4}{x^2-2x-64} & = \frac{ 16x^2 \cdot \color{blue}{ \left( x^2-2x-64 \right) }}{ \left( x+3 \right) \cdot \color{blue}{ \left( x^2-2x-64 \right) }} + \frac{ \left( 4x^5-36x^4 \right) \cdot \color{blue}{ \left( x+3 \right) }}{ \left( x^2-2x-64 \right) \cdot \color{blue}{ \left( x+3 \right) }} = \\[1ex] &=\frac{ \color{purple}{ 16x^4-32x^3-1024x^2 } }{ x^3-2x^2-64x+3x^2-6x-192 } + \frac{ \color{purple}{ 4x^6+12x^5-36x^5-108x^4 } }{ x^3-2x^2-64x+3x^2-6x-192 } = \\[1ex] &=\frac{ \color{purple}{ 4x^6-24x^5-92x^4-32x^3-1024x^2 } }{ x^3+x^2-70x-192 } \end{aligned} $$