Dividing out a variable from a quotient

I don't think I've ever mastered this concept. If I have a problem like $\frac{x+2a+3b}{x} = {4}$ , can I just divide the x out to get $1+2a+3b = 4$ ?

I know if I look at the first expression like $\frac{x}{x} + \frac{2a}{x} + \frac{3b}{x}$ then I could turn x/x into 1, but the expression would look like $1 + \frac{2a}{x} + \frac{3b}{x}$ . The x could get brought back into the quotient if it had a common denominator.

Also, if the sample problem were $\frac{x*2b+a}{x}$ would that make a difference in mathematical rules for dividing out the x? (As opposed to addition or subtraction).

I hope my question makes sense, if not I can explain more.