Question

simplifique a expressao -x²+x-1+x³+1/x+1

 

Answer 1

$- x^2 + x - 1 + x^3 + \frac{1}{x + 1} = \\\\ x^3 - x^2 + x - 1 + \frac{1}{x + 1} = \\\\ x^2(x - 1) + 1(x - 1) + \frac{1}{x + 1} = \\\\ (x - 1)[x^2 + 1] + \frac{1}{x + 1} =$

 

$\frac{(x + 1)(x - 1)(x^2 + 1) + 1}{x + 1} = \\\\ \frac{(x^2 - 1)(x^2 + 1) + 1}{x + 1} = \\\\ \frac{x^4 - 1 + 1}{x + 1} = \\\\ \boxed{\frac{x^4}{x + 1}}$