\[\frac{9}{a} - \frac{18}{a^{2} + 2a} = \frac{9}{a} - \frac{18}{a(a + 2)} =\]
\[= \frac{9(a + 2) - 18}{a(a + 2)} = \frac{9a + 18 - 18}{a(a + 2)} =\]
\[= \frac{9a}{a(a + 2)} = \frac{9}{a + 2}.\]