```
```

`#Let alpha be a primitive 10th root of unity`

alias(alpha=RootOf(X^4-X^3+X^2-X+1,X));

#We consider a rational function in 2 variables, of degree 1 in both X and Y.

num:=X^2+Y-alpha^2;den:=(alpha^3+alpha)*(X-Y-alpha);

quot:=num/den;

#Now, it would seem OK to simplify this expression.

#Note that Maple insists on making the denominator have rational coefficients.

simpquot:=simplify(quot);

#So the numerator and the denominator of this simplified expression are:

num2:=numer(simpquot);den2:=denom(simpquot);

#Let's specialise (X,Y) to (alpha^3,0). Note that the original expression is

#defined here. it is not in the conjugate point (alpha,0), though.

x:=alpha^3;y:=0;

#so, num and den are both non-zero in (X,Y)=(x,y).

simplify(subs(X=x,Y=y,[num,den]));

#num2 and den2 (of the simplified expression) are zero, though.

simplify(subs(X=x,Y=y,[num2,den2]));

#so, the quotient can be evaluated with no problem in non-simplified form.

simplify(subs(X=x,Y=y,quot));

#but in simplified form, maple does not recognise 0/0.

simplify(subs(X=x,Y=y,simpquot));