I'm a very beginner with Mathematica, and I do not get why I can't simplify this expression here:
Assuming[
{
a > 0, b > 0, c > 0, d > 0, e > 0, f > 0,
b*e - f^2 > 0,
a*e^2 - b*c*d + (f^2 - b*e)*c > 0
},
FullSimplify[
Sqrt[a*e^2 - b*c*d + (f^2 - b*e)*c]/
Sqrt[-a*e^2 + b*c*d + (-f^2 + b*e)*c]
]
]
In fact, it returns: $$\frac{\sqrt{a e^2-b c (d+e)+c f^2}}{\sqrt{-a e^2+b c (d+e)-c f^2}}$$ which is some kind of reordering of the terms, but not the full simplification. My expected result would be $-i$.
I'm assuming that everything is real, and the quantity under square root is positive.
EDIT: I've reproduced a MWE compared to original question, that was much more inricated.