\(\dfrac{2x\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}+\dfrac{\left(x-1\right)\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}+\dfrac{-3x-1}{\left(x-1\right)\left(x+1\right)}\)
\(\dfrac{2x^2-2x+x^2-x-x-2+-3x-1}{\left(x-1\right)\left(x+1\right)}\)
\(\dfrac{3x^2-7x-3}{\left(x-1\right)\left(x+1\right)}\)
\(\dfrac{3x\left(x-1\right)-7x}{\left(x-1\right)\left(x+1\right)}=\dfrac{3x-7x}{x+1}\)
\(\dfrac{2x}{x-1}+\dfrac{x-1}{x+1}-\dfrac{3x+1}{x^2-1}\) = \(\dfrac{2x\left(x+1\right)}{x^2-1}+\dfrac{\left(x-1\right)^2}{x^2-1}-\dfrac{3x+1}{x^2-1}\)
= \(\dfrac{2x^2+2x+x^2-2x+1-3x-1}{x^2-1}\)
\(=\dfrac{3x^2-3x}{x^2-1}\) \(=\dfrac{3x\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}\) \(=\dfrac{3x}{x+1}\)
