解:
$\begin{aligned}&(1-\frac{4}{a + 3})\div\frac{a^{2}-2a + 1}{2a + 6}\\=&(\frac{a + 3}{a + 3}-\frac{4}{a + 3})\div\frac{(a - 1)^{2}}{2(a + 3)}\\=&\frac{a + 3-4}{a + 3}\div\frac{(a - 1)^{2}}{2(a + 3)}\\=&\frac{a - 1}{a + 3}\cdot\frac{2(a + 3)}{(a - 1)^{2}}\\=&\frac{2}{a - 1}\end{aligned}$