\[\frac{7}{a} - \frac{56}{a^{2} + 8a} = \frac{7}{a} - \frac{56}{a(a + 8)} =\]
\[= \frac{7(a + 8) - 56}{a(a + 8)} = \frac{7a + 56 - 56}{a(a + 8)} =\]
\[= \frac{7a}{a(a + 8)} = \frac{7}{a + 8}.\]