simplifying expressions - A one line proof that one is zero using Mathematica 10

 a = (Sqrt[2] + 1) (Sqrt[2] - 1) - 1; 
 {a/a, Simplify[a]/a, b/b == Simplify[b]/b}

{1, 0, True}

This one line "proof" that one equals zero is disturbing (and could possibly lead to wrong results in real computations). Mathematica 9, unlike the versions 8 and 10, recognized that a is zero and issued a warning a/a Indeterminate!