\frac{x-0,5}{x^2-1}*\frac{(x+1)^2}{2x-1} =\frac{x-0,5}{(x+1)(x-1)}*\frac{(x+1)^2}{2x-1}= \frac{x-0,5}{x-1}*\frac{x+1}{2x-1}=
\frac{x^2+x-0,5x-0,5}{2x^2-x-2x+1}=\frac{x^2+0,5x-0,5}{2x^2-3x+1}=\frac{x^2+x-0,5x-0,5}{2(x^2-x-0,5x+0,5)}=
\frac{x(x+1)-0,5(x+1)}{2[x(x-1)-0,5(x-1)]}=\frac{(x-0,5)(x+1)}{2(x-1) (x-0,5)}=\frac{x+1}{2(x-1)}