To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $x-2$ and $2-x$ is $x-2$. Multiply $\frac{4}{2-x}$ times $\frac{-1}{-1}$.
$$\frac{x+2}{x-2}+\frac{4\left(-1\right)}{x-2}$$
Since $\frac{x+2}{x-2}$ and $\frac{4\left(-1\right)}{x-2}$ have the same denominator, add them by adding their numerators.
$$\frac{x+2+4\left(-1\right)}{x-2}$$
Do the multiplications in $x+2+4\left(-1\right)$.
$$\frac{x+2-4}{x-2}$$
Combine like terms in $x+2-4$.
$$\frac{x-2}{x-2}$$
Cancel out $x-2$ in both numerator and denominator.
