Question 248679
You were doing great until you decided to multiply by {{{2b+1}}}. If this were an equation, then you could do that (to both sides). However, you cannot do that here unless you balance that action out by also dividing by {{{2b+1}}}. So you really don't get anywhere in terms of simplification (as it makes things worse). So you're just best off stopping at the point where you got {{{(3b+1)/(2b+1)}}}



So {{{(3+b^(-1))/(2+b^(-1))=(3+1/b)/(2+1/b)=(3b+1)/(2b+1)}}} or in short,  {{{(3+b^(-1))/(2+b^(-1))=(3b+1)/(2b+1)}}}



You can verify your answer with a graph (ie the graphs of the original and the final expressions should be the same).