To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $2\left(x+1\right)$ and $1-x$ is $2\left(x+1\right)\left(-x+1\right)$. Multiply $\frac{1}{2\left(x+1\right)}$ times $\frac{-x+1}{-x+1}$. Multiply $\frac{2}{1-x}$ times $\frac{2\left(x+1\right)}{2\left(x+1\right)}$.
Since $\frac{-x+1}{2\left(x+1\right)\left(-x+1\right)}$ and $\frac{2\times 2\left(x+1\right)}{2\left(x+1\right)\left(-x+1\right)}$ have the same denominator, add them by adding their numerators.
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $2\left(x+1\right)\left(-x+1\right)$ and $4\left(x-1\right)$ is $4\left(x-1\right)\left(x+1\right)$. Multiply $\frac{3x+5}{2\left(x+1\right)\left(-x+1\right)}$ times $\frac{-2}{-2}$. Multiply $\frac{7}{4\left(x-1\right)}$ times $\frac{x+1}{x+1}$.
Since $\frac{-2\left(3x+5\right)}{4\left(x-1\right)\left(x+1\right)}$ and $\frac{7\left(x+1\right)}{4\left(x-1\right)\left(x+1\right)}$ have the same denominator, add them by adding their numerators.
