The commands a/b and Divide(a,b) return the product of a by the inverse of b. The power series b is required to be  invertible, that is, b must have a nonzero constant term.

When using the MultivariatePowerSeries package, do not assign anything to the variables occurring in the power series, Puiseux series, and univariate polynomials over these series. If you do, you may see invalid results.

$\mathrm{with}\left(\mathrm{MultivariatePowerSeries}\right)\:$

$a≔\mathrm{GeometricSeries}\left(\left[x\,y\right]\right)$

$a≔\left[\mathrm{Pow\ⅇrS\ⅇri\ⅇs\; of}\frac{1}{1-x-y}\mathrm{:}1+x+y+\mathrm{\dots }\right]$

$b≔\mathrm{PowerSeries}\left(1+x+y+z\right)$

$b≔\left[\mathrm{Pow\ⅇrS\ⅇri\ⅇs:}1+x+y+z\right]$

$c≔\frac{a}{b}$

$c≔\left[\mathrm{Pow\ⅇrS\ⅇri\ⅇs\; of}\frac{1}{\left(1-x-y\right)\left(1+x+y+z\right)}\mathrm{:}1+\mathrm{\dots }\right]$

$d≔\mathrm{Divide}\left(a\,b\right)$

$d≔\left[\mathrm{Pow\ⅇrS\ⅇri\ⅇs\; of}\frac{1}{\left(1-x-y\right)\left(1+x+y+z\right)}\mathrm{:}1+\mathrm{\dots }\right]$

$\mathrm{ApproximatelyEqual}\left(c\,d\,20\right)$

$\mathrm{true}$

The MultivariatePowerSeries[Divide] command was introduced in Maple 2021.

For more information on Maple 2021 changes, see Updates in Maple 2021.