  The exact solutions of Schr\"odinger's equation with the deformed Hulth\'en
potential $V_q(x)=-{\mu\, e^{-\delta\,x }}/({1-q\,e^{-\delta\,x}}),~
\delta,\mu, q>0$ are given, along with a closed--form formula for the
normalization constants of the eigenfunctions for arbitrary $q>0$. The
Crum-Darboux transformation is then used to derive the corresponding exact
solutions for the extended Hulth\'en potentials $V(x)= -{\mu\, e^{-\delta\,x
}}/({1-q\,e^{-\delta\,x}})+ {q\,j(j+1)\, e^{-\delta\,x
}}/({1-q\,e^{-\delta\,x}})^2, j=0,1,2,\dots.$ A general formula for the new
normalization condition is also provided.
