Question

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

Answer 1

 Olá!

 Para resolver a tarefa precisamos saber que:

$\mathbf{(a^3 - b^3) = (a - b) \cdot (a^2 + ab + b^2)}$

 Isto posto, temos que:

$\\ \displaystyle \mathsf{\frac{x^3 - 1^3}{1^2 + x^2 + (x + 1)^2} =} \\\\\\ \mathsf{\frac{(x - 1) \cdot (x^2 + x + 1)}{1 + x^2 + x^2 + 2x + 1} =} \\\\\\ \mathsf{\frac{(x - 1) \cdot (x^2 + x + 1)}{2x^2+ 2x + 2} =} \\\\\\ \mathsf{\frac{(x - 1) \cdot (x^2 + x + 1)}{2 \cdot (x^2+ x + 1)} =} \\\\\\ \boxed{\mathsf{\frac{(x - 1)}{x^2+ x + 1} }}$