Recently I am trying to understand formulas more in depth instead of just knowing them by heart.

When deriving the least squares estimators, which is Y=B0 +B1X, the B1 equals:

Σ (Xi - Xbar) (Yi-Ybar)/Σ (Xi - Xbar)^2

The thing is that this is apparently not Cov(x,y)/Var(x) because numerator and denominator are not being divided by "n-1" or simply by "n".

Therefore, why it is said Beta equals Cov(x,y)/Var(x) and not Sum of Cross products / Sum of Squares, aka SC(x,y)/SS(x)?

Thank you in advance.