simplify $\displaystyle (x^3 - 4x)/(x^3 + 2x^2)$
$\displaystyle \frac{x^3 - 4x}{x^3 + 2x^2} = \frac{x(x^2 - 4)}{x^2(x + 2)}$
$\displaystyle = \frac{x^2 - 4}{x(x + 2)}$
$\displaystyle = \frac{x^2 - 2^2}{x(x + 2)}$
$\displaystyle = \frac{(x - 2)(x + 2)}{x(x + 2)}$
$\displaystyle = \frac{x - 2}{x}$
$\displaystyle = \frac{x}{x} - \frac{2}{x}$
$\displaystyle = 1 - \frac{2}{x}$.