(\frac{x + x^{2}}{1 + x})

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

Factor $ x $ from $ x + x^2 $, get $ x(1 + x) $.

Divide $ \frac{x(1 + x)}{1 + x} $ ( $ x
eq -1 $ to avoid division by zero), cancel $ 1 + x $, result is $ x $.

$ x $ (for $ x
eq -1 $)