I'm reading a pdf document about simple linear regression, and it gave an expression of the least square estimator $\hat{\beta}\_1 = \beta\_1 + \frac{\sum^n\_{i=0} \epsilon\_i (x\_i - \bar{x})}{\sum^n\_{i=0} (x\_i - \bar{x})^2}$, but I'm confused on how they get to this answer.

I only know that $\hat{\beta}\_1 = \frac{\sum^n\_{i=0} y\_i(x\_i - \bar{x})}{\sum^n\_{i=0} (x\_i - \bar{x})^2} = \frac{\sum^n\_{i=0} (\hat{y\_i} + \epsilon\_i)(x\_i - \bar{x})}{\sum^n\_{i=0} (x\_i - \bar{x})^2}$. Does it mean $\beta\_1 = \frac{\sum^n\_{i=0} \hat{y\_i}(x\_i - \bar{x})}{\sum^n\_{i=0} (x\_i - \bar{x})^2}$? Why is that?