To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $2\left(-x-2\right)$ and $4-x$ is $2\left(-x-2\right)\left(-x+4\right)$. Multiply $\frac{3}{2\left(-x-2\right)}$ times $\frac{-x+4}{-x+4}$. Multiply $\frac{x+1}{4-x}$ times $\frac{2\left(-x-2\right)}{2\left(-x-2\right)}$.
Since $\frac{3\left(-x+4\right)}{2\left(-x-2\right)\left(-x+4\right)}$ and $\frac{\left(x+1\right)\times 2\left(-x-2\right)}{2\left(-x-2\right)\left(-x+4\right)}$ 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 $2\left(-x-2\right)$ and $4-x$ is $2\left(-x-2\right)\left(-x+4\right)$. Multiply $\frac{3}{2\left(-x-2\right)}$ times $\frac{-x+4}{-x+4}$. Multiply $\frac{x+1}{4-x}$ times $\frac{2\left(-x-2\right)}{2\left(-x-2\right)}$.
Since $\frac{3\left(-x+4\right)}{2\left(-x-2\right)\left(-x+4\right)}$ and $\frac{\left(x+1\right)\times 2\left(-x-2\right)}{2\left(-x-2\right)\left(-x+4\right)}$ have the same denominator, subtract them by subtracting their numerators.
