properties of Radon-Nikodym derivative

Question

I have two properties of the Radon-Nikodym derivative to prove:

1. $[\frac{d(\mu + \nu)}{d\lambda}] = [\frac{d\mu}{d\lambda}] + [\frac{d\nu}{d\lambda}] $
2. If $\nu \ll \mu $ and $ \mu \ll \nu$ $\to [\frac{d\mu}{d\nu}] = [\frac{d\nu}{d\mu}]^{-1}$

I started with $1$: Let $f=[\frac{d\mu}{d\lambda}]$ and $g=[\frac{d\nu}{d\lambda}]$ and then $\mu (A)=\int_{A} fd\lambda $ and $\nu(A) = \int_{A} gd\lambda$ so $\mu(A) + \nu(A) = \int_{A} fd\lambda + \int_{A} gd\lambda = \int_{A} (f+g)d\lambda = \int_{A} (\frac{d\mu}{d\lambda} + \frac{d\nu}{d\lambda})d\lambda = \int_{A} \frac{d\mu + d\nu}{d\lambda} d\lambda$

but I still don't know if it makes sense and how to go about $2$.