Simplifying Fractions Containing Variables (Basic)

I appreciate this is very simple, but I'm experiencing a very basic problem with fractions containing variables and I'd just like to check I'm along the right lines. In the following instance:

$\frac{2(x+7)(3x+1)}{2}=\frac{2}{2}\cdot \frac{2(x+7)(3x+1)}{1}=(x+7)(3x+1)$

Does the $\frac{2(x+7)(3x+1)}{1}$ have a denominator of 1 because we have factored out the 2 in the prior step?

I appreciate this is very simple, but I'm experiencing a very basic problem with fractions containing variables and I'd just like to check I'm along the right lines. In the following instance:

$\frac{2(x+7)(3x+1)}{2}=\frac{2}{2}\cdot \frac{2(x+7)(3x+1)}{1}=(x+7)(3x+1)$

Does the $\frac{2(x+7)(3x+1)}{1}$ have a denominator of 1 because we have factored out the 2 in the prior step?