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