Cancel out $x+4$ in both numerator and denominator.
$$\frac{4}{x-4}+\frac{-4}{4+x}$$
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $x-4$ and $4+x$ is $\left(x-4\right)\left(x+4\right)$. Multiply $\frac{4}{x-4}$ times $\frac{x+4}{x+4}$. Multiply $\frac{-4}{4+x}$ times $\frac{x-4}{x-4}$.
Since $\frac{4\left(x+4\right)}{\left(x-4\right)\left(x+4\right)}$ and $\frac{-4\left(x-4\right)}{\left(x-4\right)\left(x+4\right)}$ have the same denominator, add them by adding their numerators.
Cancel out $x+4$ in both numerator and denominator.
$$\frac{4}{x-4}+\frac{-4}{4+x}$$
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $x-4$ and $4+x$ is $\left(x-4\right)\left(x+4\right)$. Multiply $\frac{4}{x-4}$ times $\frac{x+4}{x+4}$. Multiply $\frac{-4}{4+x}$ times $\frac{x-4}{x-4}$.
Since $\frac{4\left(x+4\right)}{\left(x-4\right)\left(x+4\right)}$ and $\frac{-4\left(x-4\right)}{\left(x-4\right)\left(x+4\right)}$ have the same denominator, add them by adding their numerators.
