Thanks in advance!
ok so....
$\displaystyle \frac{m - \frac{1}{2m+1}}{1-\frac{m}{2m+1}}$
$\displaystyle =\frac{\frac{m(2m+1) - 1}{2m+1}}{\frac{2m+1- m}{2m+1}}$
$\displaystyle =\frac{\frac{2m^2+m - 1}{2m+1}}{\frac{m+1}{2m+1}}$
$\displaystyle =\frac{2m^2+m - 1}{2m+1}\times\frac{2m+1}{m+1}$
$\displaystyle =\frac{2m^2+m - 1}{m+1}$
Now factor the top, see what cancelations you get, and your done.