Question

Evaluate:$\frac{1-2x+x^2}{1-x^3}\times \frac{1+x+x^2}{1+x}$

Answer 1

$\frac{1-2x+x^2}{1-x^3}\times \frac{1+x+x^2}{1+x}$

$=\frac{x^2-2x+1}{1-x^3}\times \frac{x^2+x+1}{x+1}$

$=\frac{{(x-1)}^2}{(1-x)(1+x^2+x)}\times \frac{x^2+x+1}{x+1}$

$=-(x-1)\times \frac{1}{x+1}$

$=\frac{1-x}{1+x}$