Let $X$ be an integral and quasi-compact scheme. Let $\eta$ be the generic point of $X$. Let $K(X)$ be the field of rational functions of $X$ and $\operatorname{spec} (K(X)) \rightarrow X$ be the inclusion of the generic point.
Now, we define sheaf of rational functions of $K_X$ of a scheme $X$
For each open set $U$, let $S_U$ be the set of all elements in $\Gamma(U, O_X)$ that are not zero divisors in any stalk $O_{X,x}$. Let $K_{X\mathrm{pre}} $ be the presheaf whose sections on $U$ are localizations $S_U^{-1}Γ(U, O_X)$ and whose restriction maps are induced from the restriction maps of $O_X$ by the universal property of localization. Then $K_X$ is the sheaf associated to the presheaf $K_{X\mathrm{pre}}$.
The definition is mentioned here Sheaf of rational functions
Is $\Gamma(U \times_{X} \operatorname{spec}(K(X)), \mathcal{O}_{U \times_{X} \operatorname{spec}(K(X))})= \Gamma(K_U,\mathcal{O}_{K_U})$? Also why?