A= ( $\frac{1}{x-1}$ + $\frac{x}{x^3-1}$ . $\frac{x^2+x+1}{x+1}$ ) . $\frac{x^2 + 2x +1}{2x + 1}$
= (($\frac{1}{x-1}$ + $\frac{x.(x^2 +x+1)}{(x^3 -1).(x+1)}$ ). $\frac{x^2 + 2x + 1}{2x+1}$
= ($\frac{1}{x-1}$+ $\frac{x(x^2 + x+1)}{(x-1).( x^2 + x +1). (x+1)}$ ). $\frac{x^2 + 2x +1}{2x+1}$
= ($\frac{1}{x-1}$ + $\frac{x}{x^2 -1}$ ). $\frac{x^2+2x+1}{2x+1}$
= ( 2x +1 ). $\frac{x^2 + 2x +1 }{2x+1}$
= x² + 2x +1
