[tex]\displaystyle\bf\\a)~~~\frac{^{4)}x}{2x+1}=\frac{4x}{4(2x+1)}=\frac{4x}{8x+4}\\\\\\b)~~~\frac{^{x+1)}x-1}{x+1}=\frac{(x+1)(x-1)}{(x+1)(x+1)}=\frac{x^2-1}{(x+1)^2}\\\\\\c)~~~\frac{^{5)}x}{2x+1}=\frac{5x}{5(2x+1)}=\frac{5x}{10x+5}\\\\\\d)~~~\frac{^{x-1)}x-1}{x+1}=\frac{(x-1)(x-1)}{(x-1)(x+1)}=\frac{(x-1)^2}{x^2-1}[/tex]