e)
$$ \frac{1}{c^2} + \frac{2a}{6c} = \frac{3}{3c^2} + \frac{ac}{3c^2} = \frac{3 + ac}{3c^2} $$
f)
$$ \frac{\frac{1}{a}}{\frac{5}{a} + \frac{1}{a^2}} = \frac{\frac{1}{a}}{\frac{5a}{a^2} + \frac{1}{a^2}} = \frac{\frac{1}{a}}{\frac{5a + 1}{a^2}} = \frac{1}{a} \cdot \frac{a^2}{5a + 1} = \frac{1}{1} \cdot \frac{a}{5a + 1} = \frac{a}{5a + 1} $$