Numerator not recognized

Question

Here is a set of simple equations

W = 1/2 n^2 (x^2 + y^2) + 1/(2 r1) (1 + A/(2 r1^2) (1 - (3 z^2)/r1^2)) + 
1/(2 r2) (1 + A/(2 r2^2) (1 - (3 z^2)/r2^2));
n = Sqrt[1 + 3 A];
r1 = Sqrt[(x + m)^2 + y^2 + z^2];
r2 = Sqrt[(x - 1 + m)^2 + y^2 + z^2];
m = 1/2;
Wz = D[W, z] /. {x -> 0, y -> 0};

Now I want to print the simplified expression Wz and its numeratorfz.

Print["Wz = ", Simplify[Wz]]
Print["fz = ", Simplify[Numerator[Wz]]]

However Mathematica prints the same output in both cases! Why? Is this a bug?

I am using v9.0 in Windows XP 32.

Many thanks in advance!

Answer 1

You need to Simplify before taking the numerator,

Print["Wz = ", Simplify[Wz]]
Print["fz = ", Numerator[Simplify@Wz]]

The reason is that only the simplified form of Wz is a single fraction, before simplifying you have this,

Wz

and so asking for the numerator of this is the same as this simpler example

Numerator[a/b + c/b^2]
Numerator@Simplify[a/b + c/b^2]
(* a/b + c/b^2 *)
(* a b + c *)