Numerator and denominator

The f2nd or fxnd command finds the numerator and denominator of rational function after simplification.

f2nd takes rat, a rational function.
f2nd(rat) returns the list of the numerator and the denominator of the irreducible representation of rat.

f2nd((x^2-1)/(x-1))

⎡
⎣

x+1,1

⎤
⎦

f2nd((x^2+2*x+1)/(x^2-1))

⎡
⎣

x+1,x−1

⎤
⎦