\(\dfrac{2}{x-1}=\dfrac{2\left(x+1\right)\left(x-1\right)}{\left(x+1\right)\left(x-1\right)^2}=\dfrac{2x^2-2}{\left(x-1\right)^2\cdot\left(x+1\right)}\)
\(\dfrac{3x+1}{x^2-1}=\dfrac{\left(3x+1\right)\left(x-1\right)}{\left(x-1\right)^2\cdot\left(x+1\right)}\)
\(\dfrac{1}{\left(x-1\right)^2}=\dfrac{x+1}{\left(x-1\right)^2\cdot\left(x+1\right)}\)
