e) p 3p-1

е) Представим в виде дроби:

$$\frac{p}{3p-1} - \frac{p}{1+3p} = \frac{p(1+3p)}{(3p-1)(3p+1)} - \frac{p(3p-1)}{(3p-1)(3p+1)} = \frac{p + 3p^2 - (3p^2 - p)}{(3p-1)(3p+1)} = \frac{p+3p^2 - 3p^2 + p}{(3p-1)(3p+1)} = \frac{2p}{(3p-1)(3p+1)} = \frac{2p}{9p^2 - 1}.$$

Ответ: $$\frac{2p}{9p^2 - 1}$$