Hello Xaver,

Thank you very much. I noticed later that there is a bar showing up after an evaluation with the option "Simplify" on it which returned the desired result. I thank you for the explanation of why it operates the way it does. It was just puzzling to me. So much to learn, so little time.

Wolfgang

I forgot to mention that there exists another way of obtaining -3 + x^4 from your initial expression.

You can use the function Expand as

In:= Expand[x y^2/x^-3*(x y^-2/(x (y^2)^0) - 3 y^-2/x^4)]
Out= -3 + x^4

The inverse function of Expand is Factor.

In:= 1 + 2 x + x^2
Out= 1 + 2 x + x^2

In:= Factor[1 + 2 x + x^2]
Out:= (1 + x)^2

Here also, one can use Simplify to obtain the same result

In:= Simplify[1 + 2 x + x^2]
Out= (1 + x)^2

You will find in this tutorial other Wolfram Language functions that may be of use for transforming algebraic expressions.

Regards, Xavier