Answer
$x_m = \dfrac{F_{m}}{b \omega}$
Work Step by Step
The two angular frequencies equal to each other
$$ \omega = \omega_d$$
Put this expression in the given equation to get $x_m$ by
\begin{align*}
x_{m}&=\frac{F_{m}}{\left[m^{2}\left(\omega_{d}^{2}-\omega^{2}\right)^{2}+b^{2} \omega_{d}^{2}\right]^{1 / 2}}\\
&= \frac{F_{m}}{\left[m^{2}\left(\omega^{2}-\omega^{2}\right)^{2}+b^{2} \omega^{2}\right]^{1 / 2}}\\
&=\boxed{\frac{F_{m}}{b \omega}}
\end{align*}