Simplifying this complex fraction

$\displaystyle \frac{m-\frac{1}{2m+1}}{1-\frac{m}{2m+1}}$

I've done all the problems in my homework but this one, I don't even find the process difficult but something about this one is eluding me, I can't make my answer match up with the book's no matter how I work it out. Can anyone lend a hand please? :)

Re: Simplifying this complex fraction

Simplification gives you :

$\displaystyle \frac{2m^2+m-1}{m+1}=\frac{(2m-1)(m+1)}{m+1}=2m-1$

Re: Simplifying this complex fraction

I would start by multiplying by $\displaystyle \frac{2m+1}{2m+1}$

Re: Simplifying this complex fraction

Thanks guys! Really appreciate the help. I see where I was going wrong now.