If $x(t)=\displaystyle\frac{1+(x(t-T))^m}{(x(t-T)))^m}$ for all $t$
where $T$ is constant
and $x(t)=x_s$ is the solution to the above equation, why can I write that:
$x_s=\displaystyle\frac{1+{x_s}^m}{{x_s}^m}$
when on the RHS $x_s$ is evaluated at a different time?