How to convert a false fraction into the sum of an integer and a true fraction? For example, how to change the false fraction 4x + 3 / 2x + 1 into the sum of an integer and a true fraction?

How to convert a false fraction into the sum of an integer and a true fraction? For example, how to change the false fraction 4x + 3 / 2x + 1 into the sum of an integer and a true fraction?

(ax+b)/(cx+d)
If AB, then, is a false fraction
False fraction to true fraction:
Try to find a way to make the term with X in the denominator into a multiple of the denominator
Re separation of constant term
(4x+3)/(2x+1)=[2(2x+1)+1]/(2x+1)=2+1/(2x+1)