I'm not able to understand how it is that they got from 3E(e^2at)/E(e^at)^2 to the next line where they got rid of the expectation in both the numerator and the denominator and then simplified to get the final answer which I also don't understand how they simplified from the second last line. So essentially I don't understand how they worked out the expectation of the numerator term and the denominator term.
Any help would be much appreciated.
HINT
$\alpha_t$ has a normal distribution $\mathcal N (\mu,\,\sigma_{\alpha}^2)$, then $e^{\alpha_t}$ has a log-normal distribution with mean $e^{\mu+\sigma^2_{\alpha}/2}$.