Show that eqn1 equals eqn2

Hi

I am asked to show that

$\displaystyle M=\frac{m \Omega^{2}}{\sqrt{(k-m \Omega^{2})^{2}+r^{2}\Omega^{2}}}$ equals

$\displaystyle M=\frac{\beta^{2}}{\sqrt{(1-\beta^{2})^{2}+4\alpha^{2}\beta^{2}}}$ where

$\displaystyle \alpha=r/(2\sqrt{mk})$, $\displaystyle \beta=\Omega/\sqrt{k/m}$

I get the following, but I am not sure where to go or if I have made a mistake

$\displaystyle M=\frac{\beta^{2}k}{\sqrt{k(1-\beta^{2})^{2}+4\alpha^{2}k^{2}\beta^{2}}}$

Any ideas? Thanks in advance.

James