\(M=\left(\dfrac{2x}{\left(x-1\right)\left(x+1\right)}+\dfrac{x-1}{2\left(x+1\right)}\right)\cdot\dfrac{2x}{x+1}\)
\(=\dfrac{4x+x^2-2x+1}{2\left(x-1\right)\left(x+1\right)}\cdot\dfrac{2x}{x+1}\)
\(=\dfrac{\left(x+1\right)^2}{\left(x+1\right)^2}\cdot\dfrac{2x}{2\left(x-1\right)}=\dfrac{x}{x-1}\)
0<x<1 nên x-1<0 và x>0
=>M<0
=>M<|M|