You know how the numerator must be a lower degree than the denominator and if it isn't then you need to use long division/synthetic division? That's were I'm stuck. For example I tried doing long division but then I got a remainder and I'm not really sure what I'm doing.

Also it kind of confuses me when it's not just one constant on the top (e.g. A/(x-9)) how does this work? For example, if one of the factors in the numerator is then would I have ?