I have an expression:
expression=(a - 2 b + Sqrt[a^2 + 4 (b^2 + c^2) + 4 a (-b + c + 2 c d)])/(a - 2 b + 2 c + Sqrt[a^2 + 4 (b^2 + c^2) + 4 a (-b + c + 2 c d)])
that yields the following when fully simplified
FullSimplify[expression] (*(a + 2 b + 2 c + 4 a d - Sqrt[a^2 + 4 (b^2 + c^2) + 4 a (-b + c + 2 c d)])/(4 (b + a d))*)
However, the fully simplified expression is not valid for
b,d=0 whereas the original expression is.
4/7 from the original expression but is indeterminate from the mathematica fully simplified expression.
No assumptions have been made when using FullSimplify so I thought it should be true for all parameter choices. What's going wrong?