Add $ \dfrac{x^2}{x-4} $ and $ \dfrac{16}{4-x} $ to get $ \dfrac{ \color{purple}{ -x^2+16 } }{ -x+4 }$.

To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ -1 }$.

$$ \begin{aligned} \frac{x^2}{x-4} + \frac{16}{4-x} & = \frac{ x^2 \cdot \color{blue}{ \left( -1 \right) }}{ \left( x-4 \right) \cdot \color{blue}{ \left( -1 \right) }} + \frac{ 16 }{ 4-x } = \\[1ex] &=\frac{ \color{purple}{ -x^2 } }{ -x+4 } + \frac{ \color{purple}{ 16 } }{ -x+4 }=\frac{ \color{purple}{ -x^2+16 } }{ -x+4 } \end{aligned} $$

Simplify $ \dfrac{-x^2+16}{-x+4} $ to $ x+4$.

Factor both the denominator and the numerator, then cancel the common factor. $\color{blue}{x-4}$.

$$ \begin{aligned} \frac{-x^2+16}{-x+4} & =\frac{ \left( -x-4 \right) \cdot \color{blue}{ \left( x-4 \right) }}{ \left( -1 \right) \cdot \color{blue}{ \left( x-4 \right) }} = \\[1ex] &= \frac{x+4}{1} =x+4 \end{aligned} $$