# Stalk of the quotient presheaf

Consider a sheaf of abelian groupS $\mathscr F$ over a topological space $X$. If $\mathscr F'$ is a subsheaf of $\mathscr F$ (over $X$), then we can construct the quotient presheaf $\mathscr F/\mathscr F'$ in the following way:

$$(\mathscr F/\mathscr F')(U):=\mathscr F(U)/\mathscr F'(U)$$

Now I don't understand why it is true that $(\mathscr F/\mathscr F')_x=\mathscr F_x/\mathscr F'_x$ for every $x\in X$.

Notation: $\mathscr F$ is a presheaf (of abelian groups) over $X$ and $x\in X$, with the notation $\mathscr F_x$ I mean the stalk at $x$.

$\def\cF{\mathcal{F}}$ This follows from the following very nice fact:
If $\cF$ is a presheaf on $X$ and $\widetilde{\cF}$ is its sheafification, then for all $x \in X$, the natural map $\cF_x \to \widetilde{\cF}_x$ is an isomorphism.