$b)$$\frac{1-2x}{2x}$ $+$$\frac{2x}{2x-1}$ $+$$\frac{1}{2x-4x^2}$
$=$$\frac{1-2x}{2x}+$ $\frac{2x}{2x-1}+$ $\frac{-1}{2x(2x-1)}$
$=\frac{(1-2x)(2x-1)+4x^2-1}{2x(2x-1)}$
$=\frac{-4x^2+4x-1+4x^2-1}{2x(2x-1)}$
$=\frac{4x}{2x(2x-1)}=$ $\frac{2}{2x-1}$
$c)$ $\frac{1}{x-y}+$ $\frac{3xy}{y^3-x^3}+$ $\frac{x-y}{x^2+xy+y^2}=$ $\frac{x^2+xy+y^2-3xy+x^2-2xy+y^2}{(x-y)(x^2+xy+y^2)}=$ $\frac{2x^2-4xy+2y^2}{(x-y)(x^2+xy+y^2)}=$ $\frac{2(x-y)^2}{(x-y)(x^2+xy+y^2)}=$ $\frac{2(x-y)}{x^2+xy+y^2}$
$d)$$\frac{x}{x^3-1}+$ $\frac{x+1}{x^2-x}+$ $\frac{x+1}{x^2+x+1}=$ $\frac{x}{x^3-1}+$ $\frac{x+1}{x(x-1)}+$$\frac{x+1}{x^2+x+1}=$$\frac{x^2+(x+1)(x^2+x+1)+x(x-1)(x+1)}{x(x-1)(x^2+x+1)}=$ $\frac{x^2+x^3+2x^2+2x+1+x^3-x}{x(x-1)(x^2+x+1)}=$ $\frac{2x^3+3x^2+x+1}{x(x-1)(x^2+x+1)}$
