To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $\left(x-2\right)\left(x+2\right)$ and $2-x$ is $\left(x-2\right)\left(x+2\right)$. Multiply $\frac{1}{2-x}$ times $\frac{-\left(x+2\right)}{-\left(x+2\right)}$.
Since $\frac{-4}{\left(x-2\right)\left(x+2\right)}$ and $\frac{-\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}$ have the same denominator, subtract them by subtracting their numerators.
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $\left(x-2\right)\left(x+2\right)$ and $2-x$ is $\left(x-2\right)\left(x+2\right)$. Multiply $\frac{1}{2-x}$ times $\frac{-\left(x+2\right)}{-\left(x+2\right)}$.
Since $\frac{-4}{\left(x-2\right)\left(x+2\right)}$ and $\frac{-\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}$ have the same denominator, subtract them by subtracting their numerators.
Cancel out $x-2$ in both numerator and denominator.
$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{x+2})$$
If $F$ is the composition of two differentiable functions $f\left(u\right)$ and $u=g\left(x\right)$, that is, if $F\left(x\right)=f\left(g\left(x\right)\right)$, then the derivative of $F$ is the derivative of $f$ with respect to $u$ times the derivative of $g$ with respect to $x$, that is, $\frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right)$.
The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is $0$. The derivative of $ax^{n}$ is $nax^{n-1}$.
