a: \(\frac{2x}{x+1}=\frac{2x\left(x-1\right)}{\left(x+1\right)\left(x-1\right)}=\frac{2x^2-2x}{\left(x+1\right)\left(x-1\right)}\)
\(\frac{x}{x-1}=\frac{x\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}=\frac{x_{}^2+x}{\left(x-1\right)\left(x+1\right)}\)
b: \(\frac{3}{x^2+2x+1}=\frac{3}{\left(x+1\right)^2}=\frac{3\left(x-1\right)}{\left(x+1\right)^2\cdot\left(x-1\right)}=\frac{3x-3}{\left(x-1\right)\left(x+1\right)^2}\)
\(\frac{x-1}{x+1}=\frac{\left(x-1\right)\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)^2}=\frac{\left(x-1\right)\left(x^2-1\right)}{\left(x-1\right)\left(x+1\right)^2}\)
\(\frac{x^2}{x^2-1}=\frac{x^2}{\left(x-1\right)\left(x+1\right)}=\frac{x^2\left(x+1\right)}{\left(x-1\right)\left(x+1\right)^2}\)
c: \(\frac{3x+2}{x^2-2x}=\frac{3x+2}{x\left(x-2\right)}=\frac{\left(3x+2\right)\left(x+2\right)}{x\left(x-2\right)\left(x+2\right)}=\frac{3x^2+8x+4}{x\left(x-2\right)\left(x+2\right)}\)
\(\frac{1-x}{x^2-4}=\frac{1-x}{\left(x-2\right)\left(x+2\right)}=\frac{x\left(1-x\right)}{x\left(x-2\right)\left(x+2\right)}\)
