Hi there

I'm a little stuck in this one and could use a hand:

I need to show this isomorphism:

$\displaystyle (N_1+N_2)/N_2 \simeq N_1/(N_1 \cap N_2)$

Well, I make an exact sequence:

$\displaystyle 0\rightarrow N_1 \underrightarrow{\iota} (N_1 +N_2) \underrightarrow{\kappa} (N_1+N_2)/N_2 \rightarrow 0$

where $\displaystyle \iota$ is the inclusion and $\displaystyle \kappa$ the canonical mapping.

And then I find the Kernel of $\displaystyle \kappa \circ \iota$ but how do I get on from here? As far as I have understood I must find that the Kernel is exactly $\displaystyle (N_1 \cap N_2)$.