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