What is the diffrence between these three commands?

Question

Consider

F=1/((x-a)(x-b)) ; 
G= 1/((x-α)*(x-β));  
H=1/((x-r[1])(x-r[2])) ;

Using Apart[], the partial fraction decomposition is done only for $F$.

I am using version 13.1.0

What is the difference ?

Answer 1

sometimes you need to help Mathematica and tell it which is the variable to apply Apart on

F = 1/((x - a) (x - b))
G = 1/((x - α)*(x - β))
H = 1/((x - r[1]) (x - r[2]))

Compare

---

---

Basically, change Apart[G] to Apart[G, x] to make it work.

I am not sure if this is a feature or a bug but I've seen this before so may be it is a feature. If in doubt, always use the form Apart[expr,var]