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The Wolfram|Alpha result is indeed a weakness (bug).

In slightly more detail, which I hope I won't have to regret, the underlying problem is in Mathematica's Limit handling of intervals.

ee = (rho*Interval[{-1, 1}])/(rho^2*Interval[{-1, 1}] + Interval[{-1, 1}]);

In[63]:= Limit[ee, rho -> 0]

This incorrectly gives zero when it should return unevaluated.

This is a known bug. What's not known at this point is how to fix it.