Let's simplify the following expressions:

$$
\frac{a^{3}+b^{3}}{(a-b)^{2}+a b}, \quad \frac{x^{2}-4 a x+4 a^{2}}{x^{2}-4 a^{2}}, \quad \frac{x y-2 x-3 y+6}{x y-2 x}
$$
$1^{\circ}$.

$$
\frac{a^{3}+b^{3}}{(a-b)^{2}+a b}=\frac{a^{3}+b^{3}}{a^{2}-a b+b^{2}}=a+b
$$

$2^{\circ}$.

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

$3^{\circ}$.

$$
\frac{x y-2 x-3 y+6}{x y-2 x}=\frac{(x-3)(y-2)}{x(y-2)}=\frac{x-3}{x}
$$