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