解:$\frac {2m - 1}{0.25 -\mathrm {m^2}}$
$=\frac {2m - 1}{-(\mathrm {m^2} - 0.25)}$
$=\frac {2m - 1}{-(m - 0.5)(m + 0.5)}$
$=\frac {2(m - 0.5)}{-(m - 0.5)(m + 0.5)}$
$=-\frac {2}{m + 0.5},$
当$m = 2$时,原式$=-\frac {2}{2 + 0.5}$
$=-\frac {2}{2.5}$
$=-\frac {4}{5}$