I think it is fairly easy to see that
$$\frac{1}{\sqrt 2 -1} = \sqrt{2} + 1$$
Now given the fraction on the left in Maple, how can we get to the equivalent expression on the right? I apologize in advance, if this is rather obvious. But after trying a few things, I have not been able to make it work.
I have used simplify(1/(sqrt(2)-1) and simplify(1/(sqrt(2)-1) * ((sqrt(2)+1)/(sqrt(2)+1)). In both cases, Maple simply returns the first expression on the left $\frac{1}{\sqrt 2 -1}$.
Thanks to Thomas, upon looking up rationalizing the denominator, I learnt Maple has a built-in function for this purpose:
rationalize(1/(sqrt(2)-1))gives what I want. For interested reader, have a look at the documentation page here.