I don't have access to a teacher in the present moment, I just want to make sure I understand right. If I am wrong please point out where is my error, thank you.

f (x) = (2x+1) / (x-3)

y=(2x+1) / (x-3)

x=(2y+1) / (y-3)

x(y-3)=(2y+1)

xy-3x-2y=1

xy-2y=(3x+1)

y(x-2)=(3x+1)

y(x-2)/(x-2)=(3x+1)/(x-2)

y=(3x+1)/(x-2)