@nm Thanks for the advice on using =0.

But, embarassingly, I realized after posting this question, that I had mis-typed the equation into Maple. And so Maple really did the correct thing here, and I was wrongly thinking otherwise.

My equation should have read:
 equ: u2 - 2 u1 / (1-u1^2) = 0  ;; note the 2 in the numerator of the u1 rational expression.

Doh!!